A particle having a mass of \(10^{-2}\) kg carries a charge of \(5\times 10^{-8}~\mathrm{C}\). The particle is given an initial horizontal velocity of \(10^5~\mathrm{ms^{-1}}\) in the presence of electric field \(\vec{E}\) and magnetic field \(\vec{B}\) . To keep the particle moving in a horizontal direction, it is necessary that:
(a) | \(\vec{B}\) should be perpendicular to the direction of velocity and \(\vec{E}\) should be along the direction of velocity. |
(b) | Both \(\vec{B}\) and \(\vec{E}\) should be along the direction of velocity. |
(c) | Both \(\vec{B}\) and \(\vec{E}\) are mutually perpendicular and perpendicular to the direction of velocity |
(d) | \(\vec{B}\) should be along the direction of velocity and \(\vec{E}\) should be perpendicular to the direction of velocity. |
Which one of the following pairs of statements is possible?
1. | (c) and (d) |
2. | (b) and (c) |
3. | (b) and (d) |
4. | (a) and (c) |
Given below are two statements:
Statement I: | \(\overrightarrow{dl}\) of a current-carrying wire carrying a current, \(I\) is given by: \(\overrightarrow{dB}=\dfrac{\mu_0}{4\pi}~I\left(\overrightarrow{dl}\times\dfrac{\overrightarrow r}{r^3}\right )\), where \(\vec{r}\) is the position vector of the field point with respect to the wire segment. |
The magnetic field due to a segment
Statement II: | The magnetic field of a current-carrying wire is never parallel to the wire. |
1. | Statement I and Statement II are True and Statement I is the correct explanation of Statement II. |
2. | Statement I and Statement II are True and Statement I is not the correct explanation of Statement II. |
3. | Statement I is True, Statement II is False. |
4. | Statement I is False, Statement II is True. |
The correct plot of the magnitude of the magnetic field \(\vec B\) vs distance \(r\) from centre of the wire is:
(if the radius of the wire is \(R\).)
1. | 2. | ||
3. | 4. |
Assertion (A): | Work done by magnetic force on a charged particle moving in a uniform magnetic field is zero. |
Reason (R): | Path of a charged particle in a uniform magnetic field, projected in the direction of field, will be a straight line. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
Assertion (A): | \(\alpha\)-particle enter in a uniform magnetic field perpendicularly with the same speed, the time period of revolution of \(\alpha\)-particle is double to that of a proton. | If a proton and an
Reason (R): | In a magnetic field, the period of revolution of a charged particle is directly proportional to the charge of the particle and inversely proportional to the mass of the particle. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
Assertion (A): | Magnetic field interacts with a moving charge and not with a stationary charge. |
Reason (R): | A moving charge produces a magnetic field, which interacts with another magnetic field. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
Assertion (A): | If a charged particle is moving on a circular path in a perpendicular magnetic field, the momentum of the particle is not changing. |
Reason (R): | The velocity of the particle is not changing in the magnetic field. |
1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
3. | (A) is true but (R) is false. |
4. | Both (A) and (R) are false. |
Statement I: | Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element \(I(dl)\) of a current-carrying conductor only. |
Statement II: | 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. | Statement I is incorrect but Statement II is correct. |
2. | Both Statement I and Statement II are correct. |
3. | Both Statement I and Statement II are incorrect. |
4. | Statement I is correct but Statement II is incorrect. |