The following figure shows two copper rods moving with the same velocity parallel to a long straight wire carrying current. If the induced emf in rod AB is \(\mathrm{E}\), the Induced emf in rod CD is:
1. \(\mathrm{E}\)
2. \(\mathrm{E}\cos \theta\)
3. \(\mathrm{E}\sin\theta\)
4. \(0\)
1. | \(Bv^2t\) | 2. | \(2Bv^2t\) |
3. | \(\dfrac{\sqrt3}{2}Bv^2t\) | 4. | \(\dfrac{2}{\sqrt3}Bv^2t\) |
1. | \(\dfrac{2BR}{\lambda}\) | 2. | \(\dfrac{BR}{\lambda}\) |
3. | \(\dfrac{BR}{2\lambda}\) | 4. | zero |
1. | zero | 2. | \(-\dfrac{I_{0} R}{L}\) |
3. | \(\dfrac{I_{0} R}{L}\) | 4. | \(\dfrac{I_{0} R}{2L}\) |
1. | ![]() |
2. | ![]() |
3. | ![]() |
4. | ![]() |
A conducting rod of mass \(m\) and length \(l\) is free to move without friction on two parallel long conducting rails, as shown below. There is a resistance \(R\) across the rails and in the entire space around there is a uniform magnetic field \(B\) normal to the plane of the rod and the rails. The rod is given an impulsive velocity \(v_0.\)
Finally, the initial energy \(\dfrac{1}{2}mv^2_0,\)
1. | will be converted fully into heat energy in the resistor. |
2. | \(v_2\) since the rails are frictionless. | will enable the rod to continue to move with velocity
3. | will be converted fully into magnetic energy due to induced current. |
4. | will be converted into the work done against the magnetic field. |
1. | zero | 2. | \(\dfrac{\mu_{0} i}{2 \pi \left(\dfrac{R}{2}\right)}\) |
3. | \(\dfrac{1}{4}\dfrac{\mu_{0} i}{2 \pi R}\) | 4. | \(\dfrac{1}{2}\dfrac{\mu_0 i}{2\pi R}\) |
1. | zero | 2. | \(\dfrac{\mu_{0} A K}{2 \pi l}\) |
3. | \(\dfrac{\mu_{0} A K}{ \pi l}\) | 4. | \(\dfrac{2 \mu_{0} A K}{\pi l}\) |
Rings are rotated and translated in a uniform magnetic field as shown in the figure. Arrange the magnitude of emf induced across \(AB\):
1. | \(\mathrm{emf_{a}<emf_{b}<emf_{c}}\) |
2. | \(\mathrm{emf_{a}=emf_{b}<emf_{c}}\) |
3. | \(\mathrm{emf_{a}={emf}_{c}<{emf}_{b}}\) |
4. | \(\mathrm{emf_{a}<emf_{b}={emf}_{c}}\) |
1. | \(15~\text V\) | 2. | \(5~\text V\) |
3. | \(-5~\text V\) | 4. | \(-15~\text V\) |