Moving Charges and Magnetism Class 12 Physics Chapter 4 Notes

Moving Charges and Magnetism Class 12 Physics Chapter 4 Notes

History of Electricity and Magnetism

• Electricity and magnetism were known concepts for over 2000 years, but their intimate relationship was only realized around 200 years ago.
• In 1820, Danish physicist Hans Christian Oersted observed that a current in a straight wire deflected a nearby magnetic compass needle, sparking the investigation.
• Oersted found that the needle aligned tangentially to an imaginary circle with the wire as its center and perpendicular plane.
• Reversing the current direction reversed the needle’s orientation, and deflection increased with larger currents or closer proximity to the wire.
• Iron filings around the wire arranged in concentric circles, confirming the magnetic field’s presence.
• Oersted concluded that moving charges or currents produced magnetic fields in the surrounding space.
• Subsequent experimentation and discoveries led to the unification and formulation of the laws of electricity and magnetism by James Maxwell in 1864.
• Maxwell also realized that light was an electromagnetic wave.
• Radio waves were discovered by Hertz and produced by scientists like J.C. Bose and G. Marconi by the end of the 19th century.
• The 20th century saw significant scientific and technological progress due to enhanced understanding of electromagnetism and the invention of devices for producing, amplifying, transmitting, and detecting electromagnetic waves.

Sources of Magnetic Force and Fields

1. Electric Field Recap: Before discussing magnetic fields, it’s important to recap what we know about electric fields. The charge Q, which is the source of the field, creates an electric field E. This field is described by the equation:
   • E= Qr/4πϵ0​r^2​
   • Here, r is the unit vector along the direction from the charge to the point in space where the electric field is being measured.
2. Force Due to Electric Field: A charge q placed in this electric field experiences a force F, which can be calculated using the equation:
   • F=qE= qQr/4πϵ0​r2​
3. Role of Electric Field: The electric field E is not just a theoretical concept but has a physical role. It can carry energy and momentum and doesn’t propagate instantaneously; it takes time to propagate. This concept of a field was emphasized by Faraday and incorporated by Maxwell in his unification of electricity and magnetism.
4. Time Variability: Electric fields can also vary with time, meaning they can be functions of time. However, for the purposes of this chapter, it’s assumed that the fields do not change with time.
5. Superposition Principle: The field at a specific point in space can be due to one or more charges. If there are multiple charges, their fields add together vectorially. This principle of superposition holds for both electric and magnetic fields.
6. Magnetic Field (B): Similar to electric charges producing electric fields, electric currents or moving charges generate a magnetic field, denoted as B(r). The magnetic field is also a vector field and is defined at each point in space. It can also depend on time. Experimentally, it’s found that the magnetic field obeys the principle of superposition, just like the electric field.

Magnetic Field and Lorentz Force

1. Lorentz Force (F): When a point charge q is in the presence of both an electric field E(r) and a magnetic field B(r) while moving with velocity v at position r and time t, the total force (Lorentz force) acting on it can be expressed as:
   • F=q[E(r)+v×B(r)]
   • This force, combining both electric and magnetic effects, is known as the Lorentz force and was formulated by H.A. Lorentz based on experiments by Ampere and others. It can be decomposed into two components: Felectric (due to the electric field) and Fmagnetic (due to the magnetic field).
2. Characteristics of the Magnetic Force:
   • (i) Dependence on q, v, and B: The magnetic force depends on the charge of the particle (q), its velocity (v), and the magnetic field (B). The force direction is reversed for negative charges compared to positive charges.
   • (ii) Vector Product: The magnetic force q[v × B] involves a vector product (cross product) of the velocity and the magnetic field. This force becomes zero if the velocity and magnetic field are parallel or anti-parallel. It acts perpendicular to both the velocity and the magnetic field, following the right-hand rule for vector products.
   • (iii) Zero Force for Stationary Charges: The magnetic force is zero when a charge is not in motion (i.e., when the velocity |v| = 0). Only moving charges experience the magnetic force.
3. Unit of Magnetic Field (B): The expression for the magnetic force helps define the unit of magnetic field. If we set q, F, and v all to be unity (1) in the force equation F=q[v×B], where q is the angle between v and B, then the magnitude of the magnetic field (B) is one SI unit (1 T) when the force acting on a unit charge (1 C) moving perpendicular to B with a speed of 1 m/s is one newton (1 N).
   • Dimensionally, B = F/qv, and the unit of B is the tesla (T), named after Nikola Tesla (1856 – 1943).
   • A smaller unit, the gauss, is also used (1 T = 10^4 gauss).
   • For reference, the Earth’s magnetic field is approximately 3.6 × 10^(-5) T.

Magnetic Force on a Current-Carrying Conductor

1. Consideration of a Current-Carrying Rod:
   • When analyzing the magnetic force on a straight rod carrying a steady current, we consider a rod with a uniform cross-sectional area A and length l. This rod contains mobile charge carriers, such as electrons, with a number density n.
   • The total number of these mobile charge carriers in the rod is nlA.
2. Force on Charge Carriers in Magnetic Field:
   • In the presence of an external magnetic field B, the force (F) acting on these mobile charge carriers is given by: F=(nlA)q⋅vd×B
   • Here, q represents the charge of a single carrier, and vd is their average drift velocity.
3. Relating to Current Density (j) and Current (I):
   • nqvd represents the current density j, and (nqvd)A represents the total current I in the rod. Therefore: F=[jAl]×B=Il×B
   • In this equation, l is a vector with magnitude l (the length of the rod) and direction identical to the current I. It’s important to note that current I itself is not a vector.
4. Applicability to Straight Rod:
   • The equation F=Il×B holds specifically for a straight rod. Here, B is the external magnetic field acting on the rod. It’s not the magnetic field produced by the current-carrying rod itself.
5. Generalization for Arbitrary Shaped Wires:
   • If the wire has an arbitrary shape, we can calculate the Lorentz force on it by considering it as a collection of linear strips dlj​ carrying current j^j​ and summing up the contributions from each segment: F=∑(Ij​⋅dlj​×B)
   • In most cases, this summation can be converted into an integral to analyze the force on the entire wire.

Motion of a Charged Particle in a Magnetic Field

1. Work Done by Magnetic Force: In mechanics, we know that work is done on a particle when a force has a component along or opposed to the particle’s direction of motion. However, in the case of a charged particle moving in a magnetic field, the magnetic force (qv×B) is always perpendicular to the velocity of the particle. Therefore, no work is done by the magnetic force, and there is no change in the magnitude of the velocity (though the direction of momentum may change). This is different from the electric field force (qE), which can transfer energy in addition to momentum due to its parallel or antiparallel components with respect to motion.
2. Motion in a Uniform Magnetic Field:
   • When a charged particle moves in a uniform magnetic field (B), we consider the case where the velocity (v) of the particle is perpendicular to the magnetic field (B).
   • The magnetic force (qv×B) acts as a centripetal force and causes the particle to undergo circular motion perpendicular to the magnetic field.
   • The particle describes a circle if the velocity and the magnetic field are perpendicular to each other.
   • If the velocity has a component along the magnetic field (∥v∥​), this component remains unchanged as it is not affected by the magnetic field. The motion in a plane perpendicular to B remains circular, producing a helical path.
3. Centripetal Force and Radius of Circular Motion:
   • For a particle moving in a circle with radius r, a centripetal force (mv^2/r) acts perpendicular to the path toward the center.
   • When the velocity v is perpendicular to the magnetic field B, the magnetic force (qvB) also acts like a centripetal force. It has a magnitude qvB.
   • Equating the two expressions for centripetal force: mv^2/2​=qvB, we can solve for the radius r : r=mv/qB​
   • The larger the momentum (mv), the larger the radius, resulting in a larger circular path.
4. Angular Frequency and Frequency of Rotation:
   • The angular frequency (w) is related to the frequency of rotation (n) by the equation w=2πn=mqB​.
   • This relationship is independent of velocity or energy and is useful in the design of devices like cyclotrons.
5. Time Taken for One Revolution:
   • The time (T) taken for one revolution is T=2π/w​=1/n​.
6. Helical Motion with a Component Parallel to B:
   • If there is a component of velocity parallel to the magnetic field (∥v∥​), it causes the particle to move along the field, resulting in a helical path.
   • The distance moved along the magnetic field in one rotation is called the pitch (p), and it is given by p=v∥​T=2πmv∥​​/qB.
   • The radius of the circular component of motion is called the radius of the helix.

Biot-Savart Law and Magnetic Field Due to a Current Element

The Biot-Savart law describes the relationship between the current in a conductor and the magnetic field it produces. Consider a finite conductor XY carrying current I. To determine the magnetic field dB produced by an infinitesimal element dl of the conductor at a point P located at a distance r from it, with an angle q between dl and r, the Biot-Savart law states:

• The magnitude of the magnetic field dB is proportional to the current I, the element length |dl|, and inversely proportional to the square of the distance r.
• The direction of dB is perpendicular to the plane containing dl and r.

Mathematically, in vector notation:

dB ∝ Idl×r/4πr^3​

Where μ0​/4π is a constant of proportionality, and this expression holds when the medium is vacuum.

• The magnitude of the magnetic field can be calculated as:

∣dB∣=μ0​I∣dl∣sinθ/4πr^2​

Where θ is the angle between dl and r.

• This equation serves as the fundamental equation for the magnetic field produced by a current element.
• The constant of proportionality μ0​, called the permeability of free space (or vacuum), has a value of approximately 4π×10−7 Tm/A in SI units.

Comparison with Coulomb’s Law for Electric Field:

The Biot-Savart law for the magnetic field has both similarities and differences when compared to Coulomb’s law for the electric field:

(i) Long Range: Both magnetic and electric fields are long-range forces because they depend inversely on the square of the distance from the source to the point of interest. The principle of superposition applies to both fields. However, the magnetic field is linear in the source (current element I dl), just as the electric field is linear in its source (electric charge q).

(ii) Source Nature: The electric field is produced by a scalar source, which is the electric charge (q). In contrast, the magnetic field is produced by a vector source, which is the current element (I dl).

(iii) Direction of Field: The electric field is along the displacement vector joining the source and the field point. In contrast, the magnetic field is perpendicular to the plane containing the displacement vector r and the current element I dl.

(iv) Angle Dependence: The Biot-Savart law involves an angle dependence (sin q) not present in the electrostatic case.

Relation between Permittivity and Permeability of Free Space:

There’s an interesting relation between the permittivity of free space (ε0​), the permeability of free space (μ0​), and the speed of light in vacuum (c):

1/√ε0​μ0​​1=c

In SI units, μ0​ is fixed to be approximately 4π×10−7 in magnitude. Choosing the value of either ε0​ or μ0​ fixes the value of the other. This relationship is explored further in the study of electromagnetic waves.

Magnetic Field on the Axis of a Circular Current Loop

In this section, we’ll evaluate the magnetic field produced by a circular current loop along its axis. The key parameters and equations involved are as follows:

1. Setup: Consider a circular loop carrying a steady current I. The loop is located in the y-z plane, centered at the origin O, and has a radius R. The x-axis is aligned with the axis of the loop. The goal is to calculate the magnetic field at a point P on the x-axis, located at a distance x from the center O of the loop.
2. Biot-Savart Law: The magnitude dB of the magnetic field due to an infinitesimal current element dl of the loop at a point P is determined using the Biot-Savart law:
   • ∣dB∣= μ0Idl×r/4π​​r^3 ​where μ0​ is the permeability of free space.
3. Geometric Relationships:
   • r2=x2+R2, where r is the distance from the current element dl to point P.
   • The angle between dl and the displacement vector r is θ, and ∣dl×r∣=r∣dl∣sinθ.
4. Magnetic Field Components: The magnetic field dB has two components, dBx​ along the x-axis and dB⊥ perpendicular to the x-axis. Only the x-component survives, as contributions from the perpendicular components cancel out.
5. Integration: To calculate the net magnetic field along the x-axis, we integrate dBx​=dBcosθ over the entire loop.
6. Result for Magnetic Field along the Axis: Bx​=μ02Ix​​/4π(x2+R2)^3/2​
7. Special Case – Magnetic Field at the Center of the Loop:
   • At the center of the loop (x=0), the magnetic field is given by: Bi​=2Rμ0​I​
8. Direction of Magnetic Field: The direction of the magnetic field produced by the circular loop follows the right-hand thumb rule:
   • Curl the palm of your right hand around the circular wire with the fingers pointing in the direction of the current.
   • The right-hand thumb gives the direction of the magnetic field.
9. Field Lines: Magnetic field lines due to a circular wire form closed loops around the wire.

This analysis provides a way to calculate the magnetic field strength at any point along the axis of a circular current loop.

Ampere’s Circuital Law Notes

• Ampere’s Circuital Law provides an alternative representation of the Biot-Savart law.
• It deals with open surfaces with current passing through them, focusing on their boundaries.

1. Line Element and Tangential Component
   • Consider an open surface with a boundary composed of small line elements. Take one such element of length dl.
   • Multiply the tangential component of the magnetic field, Bt, at dl by its length dl (Bt dl = B · dl).
   • Sum all such products as elements get smaller, approaching an integral.
2. Ampere’s Law
   • Ampere’s law states that the integral of (B · dl) over a closed loop (boundary) is equal to μ₀ times the total current passing through the surface.
   • The integral is taken over the loop coinciding with the boundary.
   • Sign-convention: Use the right-hand rule; curl fingers in the direction of loop traversal, thumb indicates the sense of positive current.
3. Simplified Version
   • In some cases, a simplified version of Ampere’s law is applicable. It involves an amperian loop.
   • B can be: (i) Tangential and non-zero constant (B) (ii) Normal to the loop (iii) Vanishing
   • Using such loops, Ampere’s law simplifies to BL = μ₀Iₑ.
4. Applications with Symmetry
   • Ampere’s law simplifies calculations for systems with symmetry, similar to Gauss’s law for electric fields.
   • Example: Magnetic field due to an infinite straight current-carrying wire.
5. Key Points from the Example
   • Magnetic field exhibits cylindrical symmetry.
   • Field direction is tangential to concentric circles around the wire.
   • Magnetic field lines form closed loops, unlike electric field lines.
   • Field strength is finite at a non-zero distance and proportional to current and inversely proportional to distance from the wire.
   • Right-hand rule determines the field direction.
6. Relation to Biot-Savart Law
   • Ampere’s Circuital Law is analogous to Gauss’s law for electric fields.
   • It relates a boundary quantity (magnetic field) to a source quantity (current) in the interior.
   • Applicable to steady currents without time fluctuations.
7. Enclosed Current
   • Understanding “enclosed current” is crucial in applying Ampere’s law.
8. Limitations and Applicability
   • While Ampere’s Circuital Law holds for any loop, it may not always facilitate magnetic field evaluation.
   • Applicable to cases with high symmetry, making it suitable for solving problems involving systems like solenoids and toroids.

Solenoids

• A solenoid is a long cylindrical coil of wire, and in this context, we consider a “long solenoid,” which means its length is much greater than its radius.
• It is made by winding a wire in the form of a helix with closely spaced turns.
• The net magnetic field produced by a solenoid is the vector sum of the fields generated by all its individual turns.

1. Construction and Insulation
   • Solenoids are typically constructed using enamelled wires to insulate turns from each other.
2. Magnetic Field of a Finite Solenoid
   • The field between two neighboring turns forms circular loops and vanishes in this region.
   • At the interior midpoint P, the field is uniform, strong, and along the axis.
   • At the exterior midpoint Q, the field is weak and parallel to the axis with no perpendicular component.
3. Idealized Representation
   • As the solenoid becomes longer, it resembles a long cylindrical metal sheet.
   • Outside the solenoid, the magnetic field approaches zero.
   • Inside the solenoid, the magnetic field becomes everywhere parallel to the axis.
4. Application of Ampere’s Circuital Law
   • Consider a rectangular Amperian loop abcd around the solenoid.
   • Along cd and transverse sections bc and ad, the magnetic field component is zero, making no contribution to the integral.
   • Along ab, the field strength is B, where B is the relevant length of the Amperian loop (L = h).
5. Determination of Magnetic Field
   • If the number of turns per unit length is n, then the total number of turns is nh.
   • The enclosed current (Iₑ) is the product of the current in the solenoid (I) and the total number of turns (nh).
   • Applying Ampere’s circuital law, we get B × h = μ₀I × (n × h), which simplifies to B = μ₀nI.
   • The direction of the magnetic field is determined using the right-hand rule.
6. Uniform Magnetic Field
   • Solenoids are commonly used to generate a uniform magnetic field.
   • Inserting a soft iron core inside the solenoid enhances the magnetic field’s strength.

Solenoids find wide applications in electromagnets, transformers, and other devices where a controlled and strong magnetic field is required.

Ampere’s Study of Force Between Parallel Currents

• Ampere conducted studies on the magnetic force between current-carrying conductors in the early 19th century.
• He investigated how this force depends on various factors like current magnitude, conductor shape, size, and distance between conductors.

1. Two Parallel Current-Carrying Conductors
   • Consider two long parallel conductors, labeled ‘a’ and ‘b,’ separated by a distance ‘d.’
   • Conductor ‘a’ carries a current Ia, producing a magnetic field Ba at all points along conductor ‘b.’
   • The direction of Ba is downwards, as determined by the right-hand rule.
2. Force on Conductor ‘b’
   • Conductor ‘b’ (carrying current Ib) experiences a sideways force, Fba, due to the magnetic field Ba produced by ‘a.’
   • The direction of this force is toward conductor ‘a.’
   • The magnitude of Fba is given by Fba = Ib * L * Ba, where L is the length of the segment of ‘b.’
3. Force on Conductor ‘a’
   • Similarly, conductor ‘a’ experiences a force, Fab, due to the current in ‘b.’
   • Fab is equal in magnitude to Fba but directed towards ‘b’ (consistent with Newton’s third law).
4. Parallel Current Interaction
   • Parallel currents attract each other, as indicated by the forces Fba and Fab.
   • In contrast, antiparallel currents repel each other, opposite to the behavior observed in electrostatics.
5. Definition of Ampere (A)
   • The magnitude of force per unit length, fba, can be defined using the equation fba = (μ₀ * Ia * Ib) / (2πd).
   • The ampere (A) is defined as the current that, when maintained in two very long, straight, parallel conductors of negligible cross-section, placed one meter apart in a vacuum, exerts a force of 2 × 10⁻⁷ newtons per meter of length on each conductor.
   • This definition was adopted in 1946, and it serves as a theoretical basis for the ampere.
6. Relation to Coulomb
   • The SI unit of charge, the coulomb (C), can now be defined in terms of the ampere.
   • When a steady current of 1A flows through a conductor for 1 second, it carries a charge of 1 coulomb (1C).

Ampere’s work laid the foundation for understanding the interaction between current-carrying conductors and played a crucial role in establishing the SI unit of current, the ampere.

Torque on a Rectangular Current Loop in a Uniform Magnetic Field

• When a rectangular loop carrying a steady current I is placed in a uniform magnetic field, it experiences a torque, similar to the behavior of an electric dipole in an electric field.
• In this discussion, we initially consider the case when the magnetic field is in the plane of the loop.

Case 1: Magnetic Field in the Plane of the Loop

• The magnetic field B exerts no force on the arms AD and BC of the loop.
• It exerts forces F1 and F2 on arms AB and CD, respectively.
• F1 and F2 are equal in magnitude (IbB) but act in opposite directions, leading to a net force of zero.
• The torque τ on the loop due to the forces F1 and F2 is given by τ = IabB.
• The torque tends to rotate the loop anticlockwise.

Case 2: Magnetic Field at an Angle θ with the Loop

• In this general case, the angle θ between the magnetic field and the normal to the loop is not 90 degrees.
• Forces on arms BC and DA are equal, opposite, and cancel out, resulting in no net force or torque.
• Forces on arms AB and CD (F1 and F2) are also equal in magnitude (IbB) but are not collinear, creating a couple that generates torque.
• The torque τ is given by τ = IabBsinθ.
• As θ approaches 0, the perpendicular distance between the forces decreases, reducing the torque.
• When θ is either parallel or antiparallel to the magnetic field, there is no torque.

Magnetic Moment

• The magnetic moment (m) of the current loop is defined as m = IA.
• The direction of the magnetic moment is determined using the right-hand thumb rule and is into the plane of the loop.
• The torque can be expressed as τ = mBsinθ, similar to the behavior of an electric dipole in an electric field.

Units and Dimensions

• The dimensions of the magnetic moment are [A][L²], and its unit is Am².

Multiple Turns in the Loop

• If the loop has N closely wound turns, the expression for torque remains the same, with the magnetic moment given by m = NIA.

Equilibrium

• The torque vanishes when the magnetic moment is either parallel or antiparallel to the magnetic field.
• Parallel alignment indicates a stable equilibrium, while antiparallel alignment signifies an unstable equilibrium.
• This behavior explains why small magnets or magnetic dipoles align themselves with an external magnetic field.

Circular Current Loop as a Magnetic Dipole

• In this section, we explore the magnetic field produced by a circular current loop and draw an analogy with the behavior of an electric dipole in an electric field.

Magnetic Field on the Axis

• The magnitude of the magnetic field on the axis of the circular loop is given by: B ≈ (μ₀IR²) / (3x²), where x is the distance along the axis from the center of the loop.
• For x >> R, the term R² in the denominator can be dropped, simplifying the expression to B ≈ (μ₀IA) / (3x), where A = πR² is the area of the loop.

Magnetic Moment

• The magnetic moment (m) of the current loop is defined as m = IA.

Analogy with Electric Dipole

• The expression for the magnetic field B is analogous to the electric field E produced by an electric dipole: E ≈ (pe) / (4πε₀x³), where pe is the electric dipole moment and x is the distance from the dipole.
• By substituting με₀ → 1/ε₀ and m → e (electrostatic dipole) in the magnetic field expression, we obtain: B ≈ (μ₀IA) / (3x), which resembles the electric dipole field.

Further Analogy

• The analogy between the magnetic field produced by a circular current loop and the electric field of an electric dipole can be extended.
• In the electric dipole case, we found that the electric field on the perpendicular bisector of the dipole is given by E ≈ (pe) / (4πε₀x³).
• By replacing pe → m and με₀ → 1/ε₀ in the above expression, we obtain B ≈ (μ₀IA) / (3x), which is the magnetic field for a point in the plane of the loop at a distance x from the center. For x >> R, this simplifies to B ≈ (μ₀IA) / (3x).

Point Magnetic Dipole

• A planar current loop behaves like a magnetic dipole with a dipole moment m = IA, analogous to an electric dipole moment p.
• It’s important to note that magnetic monopoles (analogous to electric charges) are not known to exist.

Ampere’s Theory of Magnetism

• Ampere suggested that all magnetism is due to circulating currents, which seems partly true as magnetic monopoles haven’t been observed.
• However, elementary particles like electrons and protons carry intrinsic magnetic moments not accounted for by circulating currents.

Moving Coil Galvanometer

• The moving coil galvanometer (MCG) is an essential instrument for measuring currents and voltages in electrical circuits.

Components

• The galvanometer consists of a coil with many turns, free to rotate about a fixed axis, placed in a radial magnetic field created by a cylindrical soft iron core.
• The magnetic torque NIAB, where N is the number of turns, I is the current, A is the area of the coil, and B is the magnetic field, tends to rotate the coil.
• A spring (kf) provides a counter torque to balance the magnetic torque, resulting in a steady angular deflection (φ) of the coil.
• The deflection is indicated on a scale by a pointer attached to the spring.

Torque and Deflection

• In equilibrium, kf = NIAB.
• The deflection φ is given by the formula: φ = (NAB / k) * I (Eq. 4.38).
• The term (NAB / k) is a constant for a given galvanometer.

Usage as a Detector

• The galvanometer is used to detect the presence of current in a circuit.
• When no current flows through it, the pointer is at the neutral position in the middle of the scale.
• Depending on the direction of the current, the pointer’s deflection is either to the right or the left.

Limitations as an Ammeter

• The galvanometer is highly sensitive and gives a full-scale deflection for a current of the order of milliamps (mA).
• When connected in series to measure currents, its large resistance can affect the circuit and change the current value.
• To overcome this, a shunt resistance (rs) is connected in parallel with the galvanometer to divert most of the current.

Current Sensitivity

• The current sensitivity of the galvanometer is defined as the deflection per unit current.
• It depends on the number of turns (N), the coil area (A), and the torsional constant of the spring (k).

Usage as a Voltmeter

• The galvanometer can also be used as a voltmeter to measure voltage across a circuit section.
• When used as a voltmeter, it must draw a very small current to minimize disturbance.
• A large series resistance (R) is connected with the galvanometer to limit the current drawn.

Voltage Sensitivity

• The voltage sensitivity of the voltmeter is defined as the deflection per unit voltage.
• It depends on N, A, k, and the added series resistance (R).

Modifications for Ammeter and Voltmeter

• Converting a galvanometer into an ammeter requires adding a shunt resistance in parallel to divert most of the current.
• Converting it into a voltmeter requires adding a large series resistance in series to limit the current drawn.
• Increasing the current sensitivity may not necessarily increase the voltage sensitivity, as modifications needed for conversion can be different.