Q. No.A metallic rod of mass per unit length of \(0.5\) kgm–1 is lying horizontally on a smooth inclined plane which makes an angle of \(30^\circ\) with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction of \(0.25\) T is acting on it in the vertical direction. What is the current flowing through the rod to keep it stationary?
1.
\(7.14\) A
2.
\(5.98\) A
3.
\(14.76\) A
4.
\(11.32\) A
The current sensitivity of a moving coil galvanometer is \(5~\text{div/mA}\) and its voltage sensitivity (angular deflection per unit voltage applied) is \(20~\text{div/V}.\) The resistance of the galvanometer is:
1. \(40~\Omega\)
2. \(25~\Omega\)
3. \(250~\Omega\)
4. \(500~\Omega\)
If a square loop \({ABCD}\) carrying a current \(i\) is placed near and coplanar with a long straight conductor \({XY}\) carrying a current \(I,\) what will be the net force on the loop?
1. \(\dfrac{\mu_0Ii}{2\pi}\)
2. \(\dfrac{2\mu_0IiL}{3\pi}\)
3. \(\dfrac{\mu_0IiL}{2\pi}\)
4. \(\dfrac{2\mu_0Ii}{3\pi}\)
1. \(\frac{1}{2}\)
2. \(1\)
3. \(4\)
4. \(\frac{1}{4}\)
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. \(1~\text{MeV}\)
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. | \(\dfrac{\mu_0ne}{2\pi r}\) | 2. | zero |
| 3. | \(\dfrac{n^2e}{r}\) | 4. | \(\dfrac{\mu_0ne}{2r}\) |
| 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. | \(\dfrac{\mu_0}{2\pi d}\sqrt{\left[I^2_1+I^2_2\right ]}\) |
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