Chapter 4: Moving Charges and Magnetism Short Questions | physics Class 12 CBSE

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Chapter 4: Moving Charges and Magnetism Short Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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State two conditions under which the magnetic force on a moving charge is zero.

The magnetic force is zero when the charge is at rest (v = 0), since F = q(v × B) = 0.
The magnetic force is also zero when the velocity v is parallel or antiparallel to the magnetic field B, because the cross product v × B = 0 in this case.
Additionally, the force is zero for an uncharged particle (q = 0) regardless of its velocity or the field.

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Question 2

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Why does a magnetic force on a moving charge do no work on it?

The magnetic force q(v × B) is always perpendicular to the velocity v of the charged particle.
Work done by a force is W = F · v dt; since F is perpendicular to v, the dot product F · v = 0.
Therefore, no work is done by the magnetic force and the kinetic energy (speed) of the particle remains unchanged, though its direction may change.

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Question 3

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Define the tesla, the SI unit of magnetic field, in terms of fundamental quantities.

Tesla is defined using F = qvB sinθ: 1 tesla is the magnetic field that exerts a force of 1 newton on a charge of 1 coulomb moving at 1 m/s perpendicular to the field.
Dimensionally, [B] = [F/qv] = N s / (C m) = N / (A m), confirming its SI unit as T = kg/(A·s²).
A smaller non-SI unit, gauss, equals 10⁻⁴ T; the earth's magnetic field is approximately 3.6 × 10⁻⁵ T.

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Question 4

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State Oersted's observations and the conclusion he drew from them.

Oersted observed in 1820 that a current-carrying straight wire caused a compass needle placed nearby to deflect; the needle aligned tangentially to a circle centred on the wire.
Reversing the current direction reversed the orientation of the needle; increasing the current or bringing the needle closer increased the deflection.
He concluded that moving charges (currents) produce a magnetic field in the surrounding space.

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Question 5

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Write the expression for force on a current-carrying conductor in a magnetic field and explain the significance of each symbol.

The force on a straight conductor is F = Il × B, where I is the steady current through the conductor.
The vector l has magnitude equal to the length of the conductor (in metres) and direction along the current flow.
B is the external magnetic field; the magnitude is F = BIl sinθ, where θ is the angle between l and B.

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Question 6

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Show that the radius of the circular path of a charged particle in a uniform magnetic field is directly proportional to its momentum.

For circular motion in magnetic field B, the magnetic force provides centripetal force: qvB = mv²/r.
Solving for r gives r = mv/(qB) = p/(qB), where p = mv is the linear momentum of the particle.
Thus, r ∝ p for fixed q and B, meaning a particle with larger momentum traces a larger circle in the same magnetic field.

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Question 7

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What is the cyclotron frequency? Why is it independent of the speed of the charged particle?

Cyclotron frequency is ν = qB/(2πm), the frequency of uniform circular motion of a charged particle in a magnetic field B.
From r = mv/(qB), the time period T = 2πr/v = 2πm/(qB), so ν = 1/T = qB/(2πm).
Since neither q, B, nor m depends on v, the frequency is independent of speed—a fact exploited in the design of the cyclotron accelerator.

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Question 8

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Describe the nature of the path of a charged particle when it enters a magnetic field at an arbitrary angle (not 0° or 90°).

The velocity component perpendicular to B causes circular motion in the plane perpendicular to B, while the component parallel to B remains unchanged.
The superposition of uniform circular motion and linear motion along B results in helical (corkscrew) motion.
The radius of the helix is r = mv⊥/(qB) and the pitch (distance along B per revolution) is p = v‖ × T = 2πmv‖/(qB).

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Question 9

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State the Biot-Savart law in vector form and identify each quantity.

The Biot-Savart law states: dB = (μ₀/4π)(I dl × r)/r³, where I is the current and dl is the vector element of the conductor.
r is the displacement vector from the current element to the field point P, and r = |r| is its magnitude.
μ₀ = 4π × 10⁻⁷ T m/A is the permeability of free space; the direction of dB is perpendicular to the plane containing dl and r.

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Question 10

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Write four similarities and differences between the Biot-Savart law and Coulomb's law.

Similarity: both are long-range laws with inverse-square dependence on distance, and the principle of superposition applies to both.
Difference: the electrostatic field is produced by a scalar source (electric charge); the magnetic field is produced by a vector source (current element I dl).
Difference: the electrostatic field is along the displacement vector r; the magnetic field is perpendicular to the plane containing dl and r, with an additional sinθ dependence absent in Coulomb's law.

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Question 11

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Derive the expression for the magnetic field at the centre of a circular current loop of radius R carrying current I.

At the centre (x = 0), using the general axial formula B = μ₀IR²/[2(x²+R²)^(3/2)], substitute x = 0.
This gives B = μ₀IR²/(2R³) = μ₀I/(2R).
The direction is along the axis of the loop and determined by the right-hand thumb rule: curl fingers in the direction of current, the extended thumb points in the direction of B.

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Question 12

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State Ampere's circuital law and write its simplified form for a symmetric configuration.

Ampere's circuital law states that the line integral of the magnetic field B around any closed loop C equals μ₀ times the total current Ie passing through the surface bounded by C: ∮B·dl = μ₀Ie.
For a simplified amperian loop where B is tangential and constant in magnitude along a length L of the loop, the law reduces to BL = μ₀Ie.
The sign of Ie is determined by the right-hand rule: curl the fingers in the direction of traversal; the thumb points in the direction of positive current.

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Question 13

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Using Ampere's circuital law, find the magnetic field at a distance r outside a long straight wire carrying current I.

Choose a circular amperian loop of radius r (r > wire radius) coaxial with the wire; by symmetry B is tangential and constant along the loop.
Applying BL = μ₀Ie: B(2πr) = μ₀I.
Therefore, B = μ₀I/(2πr), showing that the field decreases inversely with distance from the wire.

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Chapter sections

Chapter 4: Moving Charges and Magnetism | Short Questions

State two conditions under which the magnetic force on a moving charge is zero.

Why does a magnetic force on a moving charge do no work on it?

Define the tesla, the SI unit of magnetic field, in terms of fundamental quantities.

State Oersted's observations and the conclusion he drew from them.

Write the expression for force on a current-carrying conductor in a magnetic field and explain the significance of each symbol.

Show that the radius of the circular path of a charged particle in a uniform magnetic field is directly proportional to its momentum.

What is the cyclotron frequency? Why is it independent of the speed of the charged particle?

Describe the nature of the path of a charged particle when it enters a magnetic field at an arbitrary angle (not 0° or 90°).

State the Biot-Savart law in vector form and identify each quantity.

Write four similarities and differences between the Biot-Savart law and Coulomb's law.

Derive the expression for the magnetic field at the centre of a circular current loop of radius R carrying current I.

State Ampere's circuital law and write its simplified form for a symmetric configuration.

Using Ampere's circuital law, find the magnetic field at a distance r outside a long straight wire carrying current I.

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