Q. No.
Moving perpendicular to field \(B\), a proton and an alpha particle both enter an area of uniform magnetic field \(B\). If the kinetic energy of the proton is \(1~\text{MeV}\) and the radius of the circular orbits for both particles is equal, the energy of the alpha particle will be:
1. \(4~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(1.5~\text{MeV}\)
4. \(1~\text{MeV}\)
1. \(4~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(1.5~\text{MeV}\)
4. \(1~\text{MeV}\)
A circuit contains an ammeter, a battery of \(30~\text{V},\) and a resistance \(40.8~\Omega\) all connected in series. If the ammeter has a coil of resistance \(480~\Omega\) and a shunt of \(20~\Omega,\) then the reading in the ammeter will be:
1. \(0.5~\text{A}\)
2. \(0.02~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)
A rectangular coil of length \(0.12~\text{m}\) and width \(0.1~\text{m}\) having \(50\) turns of wire is suspended vertically in a uniform magnetic field of strength \(0.2~\text{Wb/m}^2\). The coil carries a current of \(2~\text{A}\). If the plane of the coil is inclined at an angle of \(30^{\circ}\) with the direction of the field, the torque required to keep the coil in stable equilibrium will be:
1. \(0.15~\text{N-m}\)
2. \(0.20~\text{N-m}\)
3. \(0.24~\text{N-m}\)
4. \(0.12~\text{N-m}\)
A wire carrying current \(I\) has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to \(X\)-axis while the semicircular portion of radius \(R\) is lying in the \(Y\text-Z\) plane. The magnetic field at point \(O\) is:
1. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)
2. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)
3. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)
4. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)
An electron moving in a circular orbit of radius \(r\) makes \(n\) rotations per second. The magnetic field produced at the centre has a magnitude:
1. \(\frac{\mu_0ne}{2\pi r}\)
2. zero
3. \(\frac{n^2e}{r}\)
4. \(\frac{\mu_0ne}{2r}\)
| 1. | \({1 \over 499}G\) | 2. | \({499 \over 500}G\) |
| 3. | \({1 \over 500}G\) | 4. | \({500 \over 499}G\) |
Two identical long conducting wires \(({AOB})\) and \(({COD})\) are placed at a right angle to each other, with one above the other such that '\(O\)' is the common point for the two. The wires carry \(I_1\) and \(I_2\) currents, respectively. The point '\(P\)' is lying at a distance '\(d\)' from '\(O\)' along a direction perpendicular to the plane containing the wires. What will be the magnetic field at the point \(P?\)
| 1. | \(\dfrac{\mu_0}{2\pi d}\left(\dfrac{I_1}{I_2}\right )\) | 2. | \(\dfrac{\mu_0}{2\pi d}\left[I_1+I_2\right ]\) |
| 3. | \(\dfrac{\mu_0}{2\pi d}\left[I^2_1+I^2_2\right ]\) | 4. | \(\dfrac{\mu_0}{2\pi d}\sqrt{\left[I^2_1+I^2_2\right ]}\) |
| 1. | can be in equilibrium in one orientation |
| 2. | can be in equilibrium in two orientations, both the equilibrium states are unstable |
| 3. | can be in equilibrium in two orientations, one stable while the other is unstable |
| 4. | experiences a torque whether the field is uniform or non-uniform in all orientations |
| 1. | \(\frac{M a_0}{e} ~\text{west,}~ \frac{M a_0}{e v_0}~\text{up}\) |
| 2. | \(\frac{M a_0}{e} ~\text {west,} ~\frac{2 M a_0}{e v_0}~\text{down}\) |
| 3. | \(\frac{M a_0}{e} ~\text{east,} \frac{2 M a_0}{e v_0}~\text{up}\) |
| 4. | \(\frac{M a_0}{e} ~\text {east,} \frac{3 M a_0}{e v_0} ~\text {down}\) |
Two similar coils of radius \(R\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\) and \(2I,\) respectively. What will be the resultant magnetic field induction at the centre?
| 1. | \(\sqrt{5} \mu_0I \over 2R\) | 2. | \({3} \mu_0I \over 2R\) |
| 3. | \( \mu_0I \over 2R\) | 4. | \( \mu_0I \over R\) |
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