Moving Charges and Magnetic Field — Assertion and Reason Type

Assertion (A): Magnetic field interacts with a moving charge and not with a stationary charge.

Reason (R): A moving charge produces a magnetic field.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: The magnetic force on a charge is F = Bqv sin θ, which is zero when v = 0. A stationary charge therefore experiences no force in a magnetic field, whereas a moving charge does.

Reason (R) is also correct: Oersted's experiment showed that a magnetic field is established around a current-carrying conductor. Since electric current is charge in motion, moving charges produce a magnetic field in the surrounding space.

It is this magnetic field of the moving charge that interacts with the external magnetic field, so the Reason explains the Assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current-carrying conductor only.

Reason (R): Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: Biot-Savart law is stated for a small current-element I dl of a current-carrying conductor,

$\text{d}\vec{\text B} = \dfrac{\text µ_0}{4\text π}\dfrac{\text I(\vec{\text{dl}} \times \vec{\text r})}{\text r^3}$

To apply it to a conductor of finite size, the conductor is divided into a large number of such current-elements and the law is then integrated over the entire length.

Reason (R) is incorrect: The sources are interchanged in the statement. The charge-element dq of Coulomb's law is a scalar, while the current-element $\text I \vec{\text{dl}} \space$of Biot-Savart law is a vector whose direction is along the direction of the current.

Therefore, assertion is true but reason is false.

Assertion (A): For a point on the axis of a circular coil carrying current, magnetic field is maximum at the centre of the coil.

Reason (R): Magnetic field is inversely proportional to the distance of point from the circular coil.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: At a point on the axis of a circular coil at a distance x from the centre,

$\text B = \dfrac{\text µ_0}{4\text π}\dfrac{2\text{πNIa}^2}{(\text a^2 + \text x^2)^{3/2}}$

This has its largest value at x = 0, where it becomes $\text B = \dfrac{\text µ_0 \text{NI}}{2\text a}$. Hence the field is maximum at the centre of the coil.

Reason (R) is incorrect: Every element of the coil is at a distance $\text d = \sqrt{\text a^2 + \text x^2}$ from the point, so the field above can be written $\text B = \dfrac{\text µ_0 \text{NIa}^2}{2\text d^3}$. The field varies as $\dfrac{1}{\text d^3}$, not inversely as the distance; it is still greatest at the centre, where d is least.

Therefore, assertion is true but reason is false.

Note: The printed answer key gives option 1 (both true, with R explaining A), but the axial-field relation shows that B is not inversely proportional to the distance, so option 3 is the correct choice.

Assertion (A): The direction of force on a moving charge is given by Fleming's left hand rule.

Reason (R): A magnetic field exerts a force on a moving charge in the same direction as the direction of field itself.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: For a moving charge the direction of the force is given by Fleming's left-hand rule. In applying it, the direction of motion of a positively charged particle is taken as the direction of current, and for a negatively charged particle the direction of current is opposite to its direction of motion.

Reason (R) is incorrect: The magnetic force is given by $\vec{\text F} = \text q(\vec{\text v} \times \vec{\text B})$, so it is always perpendicular to the magnetic field, never along it. A force along the direction of the field is a property of the electric field, not of the magnetic field.

Therefore, assertion is true but reason is false.

Assertion (A): When a charged particle moves perpendicular to magnetic field then its kinetic energy and momentum get affected.

Reason (R): Force changes velocity of charged particle.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are false.

Explanation

Assertion (A) is incorrect: When a charged particle moves perpendicular to a magnetic field, the force acting on it is always perpendicular to its velocity. Such a force does no work, so the speed and hence the kinetic energy of the particle remain unchanged.

Reason (R): Taken literally the Reason is true, since the magnetic force changes the direction of the velocity; it does not, however, change its magnitude.

Therefore, the assertion is false, and option 4 is the only option consistent with that (see Note).

Note: The momentum of the particle does change, because the direction of its velocity changes continuously. The option scheme offers no 'assertion false, reason true' choice; since the Assertion is false, option 4 (the printed key) is the only consistent choice, and it treats R as a claim about the magnitude of the velocity.

Assertion (A): The kinetic energy of a charged particle moving in a uniform magnetic field does not change.

Reason (R): In a uniform magnetic field no force acts on the charged particle.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: The magnetic force on the particle acts perpendicular to its direction of motion, so no work is done by the field on the particle. Its speed, and hence its kinetic energy, remains the same.

Reason (R) is incorrect: A force does act on the charged particle in a uniform magnetic field, given by F = Bqv sin θ. It is not zero (except when θ = 0 or 180°); it is merely always perpendicular to the velocity.

Therefore, assertion is true but reason is false.

Assertion (A): The mass of proton is 1837 times more than the mass of electron.

Reason (R): An electron and proton enters a magnetic field with equal velocities, then the force experienced by proton will be more than electron.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: The mass of a proton is about 1837 times the mass of an electron.

Reason (R) is incorrect: The magnetic force is

$\text F = \text{Bqv} \sin \text θ$

which is independent of the mass of the particle. As the electron and the proton carry charges of equal magnitude and enter the field with equal velocities, both experience forces of the same magnitude.

Therefore, assertion is true but reason is false.

Assertion (A): The magnetic field at the ends of a very long current-carrying solenoid is half of that at the centre.

Reason (R): If the solenoid is sufficiently long, the field within it is uniform.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true but reason is not the correct explanation of assertion.

Explanation

Assertion (A) is correct: For a long solenoid the field well inside is B = µ₀nI₀, while at the ends only one half of the winding contributes, giving

$\text B_{\text{end}} = \dfrac{1}{2}\text µ_0 \text n \text I_0$

Reason (R) is also correct: The magnetic lines of force inside a long solenoid are straight, parallel and equidistant, showing a uniform magnetic field, except near the edges.

The uniformity of the field inside, however, does not by itself explain why the field at the ends falls to half its value; that follows from the loss of the winding on one side. Hence the Reason does not explain the Assertion.

Therefore, both assertion and reason are true but reason is not the correct explanation of assertion.

Assertion (A): The magnetic field produced by a current-carrying solenoid is independent of its length and cross-sectional area.

Reason (R): The magnetic field inside the solenoid is uniform.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true but reason is not the correct explanation of assertion.

Explanation

Assertion (A) is correct: For a long solenoid,

$\text B = \text µ_0 \text n \text I_0$

where n is the number of turns per unit length. The expression contains neither the length nor the area of cross-section of the solenoid, so the field is independent of both.

Reason (R) is also correct: The field inside a long solenoid is uniform over the cross-section and along the axis, except near the edges.

The uniformity of the field is a separate property; the independence of B from the length and the area follows from the application of Ampere's circuital law to the rectangular path. Hence the Reason does not explain the Assertion.

Therefore, both assertion and reason are true but reason is not the correct explanation of assertion.

Assertion (A): If a proton and an α-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of α-particle is doubled that of proton.

Reason (R): In a magnetic field, the period of revolution of a charged particle is directly proportional to the mass of the particle and is inversely proportional to its charge.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: For a proton m_p = m and q_p = e, while for an α-particle m_α = 4m and q_α = 2e. Hence

$\dfrac{\text T_\text p}{\text T_α} = \dfrac{\text m_\text p}{\text q_\text p} \times \dfrac{\text q_α}{\text m_α} \\[1em] \dfrac{\text T_\text p}{\text T_α} = \dfrac{\text m}{\text e} \times \dfrac{2\text e}{4\text m} \\[1em] \dfrac{\text T_\text p}{\text T_α} = \dfrac{1}{2} \\[1em] \text T_α = 2\text T_\text p$

Reason (R) is also correct: The period of revolution of a charged particle in a magnetic field is

$\text T = \dfrac{2\text{πm}}{\text{qB}}$

so T is directly proportional to the mass and inversely proportional to the charge. Substituting the masses and charges of the two particles in this relation gives the result of the Assertion directly.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): Magnetic force is always perpendicular to the magnetic field.

Reason (R): Electric force is along the direction of electric field.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true but reason is not the correct explanation of assertion.

Explanation

Assertion (A) is correct: The magnetic force $\vec{\text F} = \text q(\vec{\text v} \times \vec{\text B})$ is perpendicular to the plane containing $\vec{\text v} \space$and $\vec{\text B} \space$, so it is always perpendicular to the magnetic field.

Reason (R) is also correct: The electric force on a charge is $\vec{\text F} = \text q\vec{\text E}$, which is along the direction of the field for a positive charge and opposite to it for a negative charge.

The behaviour of the electric force is a statement about a different field, so it cannot explain why the magnetic force is perpendicular to $\vec{\text B} \space$.

Therefore, both assertion and reason are true but reason is not the correct explanation of assertion.

Assertion (A): The energy of charged particle moving in a uniform magnetic field does not change.

Reason (R): Work done by magnetic field on the charge is zero.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: The force on a charged particle moving in a uniform magnetic field always acts in a direction perpendicular to the direction of motion of the charge, so the speed of the particle does not change and its energy remains the same.

Reason (R) is also correct: Since the force is perpendicular to the displacement, the work done by the magnetic field on the charge is

$\text W = \text{FS} \cos 90° \\[1em] \text W = 0$

As no work is done on the particle, its energy cannot change. Hence the Reason explains the Assertion.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Note: The printed answer key gives option 4 (both false), but the book's own explanation states that the work done by the magnetic field is zero and therefore the energy of the charged particle does not change. Both statements are true and the Reason explains the Assertion, so the correct choice is option 1.

Assertion (A): The kinetic energy does not change when a particle is moving in a uniform magnetic field.

Reason (R): The velocity of the particle is not affected by magnetic field.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: The magnetic force acts perpendicular to the velocity, so it does no work on the particle. The speed, and hence the kinetic energy, remains unchanged.

Reason (R) is incorrect: The velocity of the particle is certainly affected by the magnetic field. Only the magnitude of the velocity stays constant; its direction changes continuously, which is why the particle moves along a circular path.

Therefore, assertion is true but reason is false.

Assertion (A): A charged particle can be accelerated in a cyclotron by the alternate distribution of the field.

Reason (R): Energy of charged particle is increased by the field applied.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: In a cyclotron an alternating potential difference is applied across the dees, so that each time the particle crosses the gap the field has reversed and always accelerates it. By repeating the process again and again the particle is accelerated to high energies.

Reason (R) is also correct: Each crossing of the gap increases the kinetic energy of the particle by qV, so the energy of the charged particle is increased by the applied field. The magnetic field brings the particle back to the gap again and again for this repeated acceleration.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.

Assertion (A): Magnetic lines form closed loops in nature.

Reason (R): Mono-magnetic pole exist in nature.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If assertion is true but reason is false.

Explanation

Assertion (A) is correct: Magnetic lines of force form closed loops, unlike electrostatic lines of force which originate from a positive charge and end on a negative charge.

Reason (R) is incorrect: A mono-magnetic pole (magnetic monopole) does not exist in nature. It is precisely because isolated poles do not exist that the magnetic lines have to close on themselves.

Therefore, assertion is true but reason is false.

Assertion (A): A proton and an electron, with same momenta, enter in a uniform magnetic field in a direction at right angles to the lines of force. The radius of the path followed by them will be same.

Reason (R): Electron has less mass than the proton.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true but reason is not the correct explanation of assertion.

Explanation

Assertion (A) is correct: The radius of the path followed by a charged particle entering a magnetic field at right angles is

$\text r = \dfrac{\text p}{\text{qB}}$

The proton and the electron have the same momentum p, charges of equal magnitude q and move in the same field B, so the radii of their paths are equal.

Reason (R) is also correct: The electron does have a much smaller mass than the proton.

The masses, however, do not enter the expression for r once the momentum is fixed, so the Reason is not the correct explanation of the Assertion.

Therefore, both assertion and reason are true but reason is not the correct explanation of assertion.

Assertion (A): The poles of a bar magnet cannot be separated.

Reason (R): Magnetic monopoles do not exist.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true but reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.

Answer

If both assertion and reason are true and reason is the correct explanation of assertion.

Explanation

Assertion (A) is correct: However small the pieces into which a bar magnet is broken, each piece is found to be a complete magnet with a north and a south pole. The poles cannot be separated from each other.

Reason (R) is also correct: Magnetic monopoles do not exist. According to Gauss' law of magnetism, the magnetic flux through any closed surface is

$\text φ = \sum_{\text{all area elements}} \vec{\text B} \cdot \vec{\Delta \text S} = 0$

which shows that an isolated magnetic pole cannot exist. This is exactly why the poles of a bar magnet cannot be separated.

Therefore, both assertion and reason are true and reason is the correct explanation of assertion.