Q. No.By which relation is the deflection of the coil \(\theta\) related to the electrical current \(i\) in a moving coil galvanometer?
1. \(i \propto \tan \theta\)
2. \(i \propto \theta\)
3. \(i \propto \theta^{2}\)
4. \(i \propto \sqrt{\theta}\)
Three long, straight, and parallel wires carrying currents of \(30\) A, \(10\) A, and \(20\) A in \(P\), \(Q\), and \(R\), respectively, are arranged as shown in the figure. What is the force experienced by a \(10\) cm length of wire \(Q\)?
| 1. | \(1.4 \times 10^{-4}~\text{N}\) towards the right |
| 2. | \(1.4 \times 10^{-4}~\text{N}\) towards the left |
| 3. | \(2.6 \times 10^{-4}~\text{N}\) to the right |
| 4. | \(2.6 \times 10^{-4}~\text{N}\) to the left |
When a positively charged particle moves in an \(x\text-y\) plane, its path abruptly changes due to the presence of electric and/or magnetic fields beyond \(P\). The curved path is depicted in the \(x\text-y\) plane and is discovered to be noncircular. Which of the following combinations is true?
1. \(\vec{{E}}=0 ; \vec{{B}}={b} \hat{i}+{c} \hat{k}\)
2. \(\vec{E}={a\hat{i}} ; \vec{B}={c} \hat{k}+a\hat{i}\)
3. \(\vec{E}=0 ; \vec{B}=c \hat{j}+b \hat{k}\)
4. \(\vec{E}=a\hat i ; \vec{B}=c\hat{k}+{b}\hat{j}\)
Two insulated rings, one of a slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially, the planes of the rings are mutually perpendicular. What happens when a steady current is set up in each of them?
| 1. | the two rings rotate into a common plane. |
| 2. | the inner ring oscillates about its initial position. |
| 3. | the inner ring stays stationary while the outer one moves into the plane of the inner ring. |
| 4. | the outer ring stays stationary while the inner one moves into the plane of the outer ring. |
A charge \(Q\) is uniformly distributed on a ring of radius \(R\) made of an insulating material. If the ring rotates about the axis passing through its centre and normal to the plane of the ring with constant angular speed \(\omega\), then what will be the magnitude of the magnetic moment of the ring?
1. \(Q \omega R^{2}\)
2. \(\frac{1}{2} Q \omega R^{2}\)
3. \(Q \omega^{2} R\)
4. \(\frac{1}{2} Q\omega^{2} R\)
| 1. | \(10^{-5} ~\text{N} \), attractive |
| 2. | \(10^{-5}~\text{N} \), repulsive |
| 3. | \(2 \times 10^{-5}~\text{N} \), attractive |
| 4. | \(2 \times 10^{-5} ~\text{N} \), repulsive |
\(\left(\mu_0= 4\pi \times 10^{-7}~\text{weber/(amp-m)}\right)\)
| 1. | Repulsive force of \(10^{-4}~\text{N/m}\) |
| 2. | Attractive force of \(10^{-4}~\text{N/m}\) |
| 3. | Repulsive force of \(2 \pi \times 10^{-5}~\text{N/m}\) |
| 4. | Attractive force of \(2 \pi \times 10^{-5}~\text{N/m}\) |
1. \(\frac{\sigma_{i}}{G} = \sigma_{v}\)
2. \(\frac{\sigma_{v}}{G} =\sigma_{i}\)
3. \(\frac{G}{\sigma_{v}} =\sigma_{i}\)
4. \(\frac{G}{\sigma_{i}} =\sigma_{v}\)
| 1. | putting in series resistance of \(240 ~\Omega \text {. }\) |
| 2. | putting in parallel resistance of \(240 ~\Omega \text {. }\) |
| 3. | putting in series resistance of \(15~ \Omega \text {. }\) |
| 4. | putting in parallel resistance of \(15~ \Omega \text {. }\) |
| 1. | \(nB\) | 2. | \(n^2B\) |
| 3. | \(2nB\) | 4. | \(2n^2B\) |
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