When a \(12~\Omega\) resistor is connected in parallel with a moving coil galvanometer, its deflection reduces from \(50\) divisions to \(10\) divisions. What will be the resistance of the galvanometer?
1. \(24~\Omega\)
2. \(36~\Omega\)
3. \(48~\Omega\)
4. \(60~\Omega\)
Which of the following graphs correctly represents the variation of magnetic field induction with distance due to a thin wire carrying current?
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4. | ![]() |
1. | \(M\) | 2. | \(\sqrt{2} M\) |
3. | \(3 M\) | 4. | \(2 M\) |
Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?
1. | \(\frac{{i} \Delta {l} \sin (\theta)}{{r}^2} \) | 2. | \(\frac{\mu_0}{4 \pi} \frac{i \Delta {l} \sin (\theta)}{r} \) |
3. | \(\frac{\mu_0}{4 \pi} \frac{{i} \Delta{l} \sin (\theta)}{{r}^2} \) | 4. | \(\frac{\mu_0}{4 \pi} {i} \Delta {l} \sin (\theta)\) |
What is the magnetic field at point \(O\) in the figure?
1. | \(\dfrac{\mu_{0} I}{4 \pi r}\) | 2. | \(\dfrac{\mu_{0} I}{4 \pi r} + \dfrac{\mu_{0} I}{2 \pi r}\) |
3. | \(\dfrac{\mu_{0} I}{4 r} + \dfrac{\mu_{0} I}{4 \pi r}\) | 4. | \(\dfrac{\mu_{0} I}{4 r} - \dfrac{\mu_{0} I}{4 \pi r}\) |
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A current-carrying wire is placed in a uniform magnetic field in the shape of the curve \(y= \alpha \sin \left({\pi x \over L}\right),~0 \le x \le2L.\)
What will be the force acting on the wire?
1. | \(iBL \over \pi\) | 2. | \(iBL \pi\) |
3. | \(2iBL \) | 4. | zero |
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2. | ![]() |
3. | ![]() |
4. | ![]() |
A particle of charge \(+q\) and mass \(m\) moving under the influence of a uniform electric field \(E\hat i\) and a uniform magnetic field \(\mathrm B\hat k\) follows a trajectory from \(P\) to \(Q\) as shown in the figure. The velocities at \(P\) and \(Q\) are \(v\hat i\) and \(-2v\hat j\) respectively. Which of the following statement(s) is/are correct?
1. | \(E=\frac{3}{4} \frac{{mv}^2}{{qa}}\). |
2. | Rate of work done by electric field at \(P\) is \(\frac{3}{4} \frac{{mv}^3}{a}\). |
3. | Rate of work done by both fields at \(Q\) is zero. |
4. | All of the above. |