Chapter summary — Moving Charges & Magnetism
This chapter explores magnetic effects produced by moving charges and currents. Key topics: magnetic field due to a moving charge and current element (Biot–Savart law), Ampère's circuital law, force on a moving charge (Lorentz force) and on a current-carrying conductor, motion of charged particles in uniform magnetic fields (circular/helix), magnetic dipole and torque on a current loop, magnetic moment, cyclotron, moving charges in combined electric and magnetic fields, Hall effect and its applications. Important formulas: F = q(v × B), dB = (μ0/4π)(Idℓ × r̂)/r^2, torque τ = μ × B, radius r = mv/qB, cyclotron frequency ω = qB/m.
Revision tips: Practice vector cross-product direction (right-hand rule), derive radius/time period of circular motion in B, use Biot–Savart for simple geometries and Ampère for symmetric cases, and memorize Hall voltage expression V_H = (IB)/(net) sign convention.
1. Lorentz force acting on a charge q moving with velocity v in a magnetic field B is given by:
A) q(v·B)
B) q(v × B) ✅
C) qE
D) q(v + B)
2. The magnetic force on a charged particle is maximum when v is _____ to B.
A) Perpendicular ✅
B) Parallel
C) At 45°
D) Zero
3. A charged particle moving perpendicular to a uniform magnetic field follows a:
A) Straight line
B) Circular path ✅
C) Parabolic path
D) Elliptical path
4. Radius of circular path of charge q with mass m and speed v in magnetic field B is:
A) mv/qB ✅
B) qB/mv
C) m/qvB
D) v/ m q B
5. Time period of revolution for charged particle in uniform B is independent of:
A) Magnetic field
B) Speed (for given B and q/m) ✅
C) Charge
D) Mass
6. Motion of a charged particle in combined electric E and magnetic B fields can be straight line if:
A) E = 0
B) E = v × B (velocity selector) ✅
C) v = 0
D) E parallel to B
7. Biot–Savart law gives magnetic field due to:
A) A point charge at rest
B) A steady current element ✅
C) Electric dipole
D) Magnetic monopole
8. Magnetic field at the center of a circular loop of radius R carrying current I is:
A) μ0 I / (2R) ✅
B) μ0 I / R
C) μ0 I / (4πR)
D) 0
9. SI unit of magnetic field B (magnetic flux density) is:
A) Tesla (T) ✅
B) Weber
C) Henry
D) Gauss
10. Ampère's circuital law is most useful for calculating B when:
A) There is no symmetry
B) High symmetry (e.g., infinite straight wire, solenoid) ✅
C) Charges are static
D) Medium is non-magnetic only
11. Magnetic field inside an ideal long solenoid (n turns per unit length) carrying current I is:
A) μ0 n I ✅
B) μ0 I / n
C) μ0 n / I
D) 0
12. Force on a current-carrying wire of length L in magnetic field B when current I flows is:
A) I L · B
B) I (L × B) ✅
C) q(v × B)
D) Zero
13. Right-hand rule gives direction of:
A) Electric field
B) Magnetic force and field orientation for currents ✅
C) Gravitational force
D) Temperature gradient
14. Hall effect is used to determine:
A) Electric field only
B) Sign of charge carriers and carrier density ✅
C) Mass of electron
D) Magnetic susceptibility
15. Hall voltage V_H across a conductor is proportional to:
A) Current and magnetic field and inverse of carrier density ✅
B) Square of current
C) Only magnetic field
D) Only carrier density
16. Magnetic dipole moment μ of a current loop is given by:
A) I / A
B) I × area (IA) ✅
C) I × length
D) IA/2
17. Torque τ experienced by a magnetic dipole in uniform B is:
A) μ × B ✅
B) μ · B
C) q(v × B)
D) Zero always
18. Magnetic field at a distance r from a long straight current I is:
A) μ0 I / (2π r) ✅
B) μ0 I / r
C) μ0 I / (4π r^2)
D) Zero
19. A charged particle entering a magnetic field with velocity component parallel to B will:
A) Move in a helix (circular + translation) ✅
B) Deflect at right angle only
C) Stop
D) Reverse
20. Magnetic field due to a current loop at its centre is proportional to:
A) I/R ✅
B) I·R
C) R/I
D) I²/R
21. In SI units, permeability of free space μ0 equals:
A) 4π × 10^-6 N/A^2 ✅
B) 4π × 10^-7 N/A^2
C) 10^-7 N/A^2
D) 1
22. Magnetic field at the centre of a long straight solenoid of n turns per unit length and current I is:
A) μ0 n I ✅
B) μ0 I / n
C) μ0 n / I
D) 0
23. Biot–Savart law contains which physical constant?
A) Permittivity ε0
B) Permeability μ0 ✅
C) Planck's constant
D) Speed of light
24. Magnetic lines of force around a straight current are:
A) Concentric circles centered on the wire ✅
B) Radial lines
C) Straight lines parallel to wire
D) Helical
25. Force between two parallel currents I1 and I2 separated by distance r is:
A) Attractive if currents are in same direction (μ0 I1 I2 / 2π r) ✅
B) Repulsive for same direction
C) Zero always
D) Depends on voltage
26. In a velocity selector, only particles with velocity v = E/B pass undeflected. This device uses:
A) Perpendicular E and B fields ✅
B) Parallel E and B
C) Only B
D) Only E
27. Cyclotron frequency (angular) ω for a particle with charge q and mass m in magnetic field B is:
A) qB/m ✅
B) m/qB
C) q/m
D) B/mq
28. In Hall effect, if carriers are electrons, Hall coefficient R_H is:
A) Positive
B) Negative (−1/ne) ✅
C) Zero
D) Infinite
29. Magnetic field inside an ideal toroid is:
A) μ0 N I / (2π r) (inside) ✅
B) Zero everywhere
C) μ0 I / (2R)
D) Infinite
30. A magnetic dipole in a uniform magnetic field experiences:
A) Torque but no net force ✅
B) Net force only
C) Both force and torque
D) No effect
31. SI unit of magnetic dipole moment is:
A) A·m^2 ✅
B) T·m^2
C) N·m
D) Wb
32. Magnetic flux density B and magnetic field H are related by:
A) B = μ0 (H + M) or B = μ H ✅
B) B = ε0 H
C) B = μ0 / H
D) B = H/μ
33. The SI unit of magnetic flux (Φ) is:
A) Weber (Wb) ✅
B) Tesla
C) Henry
D) Ampere
34. Magnetic field at the center of a semicircular current-carrying wire of radius R is:
A) μ0 I / (4R) ✅
B) μ0 I / (2R)
C) μ0 I / (π R)
D) μ0 I / (8R)
35. In a cyclotron, particles are accelerated across a gap by an alternating electric field while magnetic field makes them follow:
A) Circular arcs of increasing radius ✅
B) Straight lines
C) Helical paths
D) Random motion
36. Magnetic field at a distance r on the axis of a circular loop of radius R (center at origin) is:
A) μ0 I R^2 / (2 (R^2 + r^2)^(3/2)) ✅
B) μ0 I / (2π r)
C) μ0 I / (2R)
D) Zero
37. For a charged particle in magnetic field, magnetic force does no work because:
A) Force is perpendicular to velocity ✅
B) Force is parallel to velocity
C) Force is zero
D) Particle has no kinetic energy
38. Magnetic moment of an electron orbiting nucleus (classical) is proportional to:
A) Current × area (related to angular momentum) ✅
B) Mass only
C) Charge only
D) Radius only
39. When an electron beam enters a region of uniform magnetic field perpendicular to its velocity, the beam:
A) Bends into a circular path ✅
B) Continues straight
C) Splits
D) Speeds up
40. Magnetic field due to an infinite sheet of current (surface current K) at a point near it is:
A) μ0 K / 2 ✅
B) μ0 K
C) μ0 K / (4π)
D) Zero
41. Magnetic field produced by a finite straight segment at a point on its perpendicular bisector involves:
A) Biot–Savart integral (depends on angle subtended) ✅
B) Coulomb's law
C) Gauss's law
D) Ohm's law
42. A charged particle moving parallel to magnetic field experiences:
A) No magnetic force (moves undeflected) ✅
B) Maximum force
C) Circular motion
D) Helical motion
43. The direction of magnetic field at a point on axis of circular loop is given by:
A) Along axis given by right-hand rule (thumb direction) ✅
B) Radial
C) Tangential
D) Opposite to current always
44. Magnetic susceptibility is a measure of:
A) How much a material becomes magnetized in a magnetic field ✅
B) Electrical conductivity
C) Thermal conductivity
D) None
45. Magnetic field inside an ideal long straight conductor carrying uniform current is:
A) μ0 I r / (2π R^2) (varies with r) ✅
B) μ0 I / (2π r)
C) Zero
D) Independent of r
46. If current in a loop is reversed, the magnetic dipole moment:
A) Reverses sign ✅
B) Doubles
C) Unchanged
D) Goes to zero
47. Magnetic field due to a pair of Helmholtz coils is nearly uniform at:
A) Midpoint between the coils when separated by radius ✅
B) Far away from coils
C) Only outside coils
D) Never uniform
48. Magnetic moment of a current loop is maximum when the plane of the loop is _____ to the magnetic field.
A) Perpendicular ✅
B) Parallel
C) At 45°
D) Random
49. A current element Idℓ at a point produces magnetic field dB proportional to:
A) Idℓ × r̂ / r^2 (Biot–Savart) ✅
B) Idℓ · r̂ / r^2
C) Idℓ / r
D) Idℓ / r^3
50. Magnetic field inside an ideal infinite solenoid is independent of:
A) Radial position inside solenoid (uniform inside) ✅
B) Current
C) Number of turns per unit length
D) Permeability