A wire cd of length \(l\) and mass \(m\) is sliding without friction on conducting rails \(ax\) and \(by\) as shown. The vertical rails are connected to each other with a resistance \(R\) between \(a\) and \(b\). A uniform magnetic field \(B\) is applied perpendicular to the plane \(abcd\) such that \(cd\) moves with a constant velocity of:
1. | \({mgR \over Bl}\) | 2. | \({mgR \over B^2l^2}\) |
3. | \({mgR \over B^3l^3}\) | 4. | \({mgR \over B^2l}\) |
A coil having number of turns \(N\) and cross-sectional area \(A\) is rotated in a uniform magnetic field \(B\) with an angular velocity \(\omega\). The maximum value of the emf induced in it is:
1. \(\frac{NBA}{\omega}\)
2. \(NBAω\)
3. \(\frac{NBA}{\omega^{2}}\)
4. \(NBAω^{2}\)
A long solenoid has \(1000\) turns. When a current of \(4\) A flows through it, the magnetic flux linked with each turn of the solenoid is \(4\times 10^{-3}\) Wb. The self-inductance of the solenoid is:
1. \(3\) H
2. \(2\) H
3. \(1\) H
4. \(4\) H
A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is:
1. | Twice per revolution | 2. | Four times per revolution |
3. | Six times per revolution | 4. | Once per revolution |
The current \(i\) in an inductance coil varies with time \(t\) according to the graph shown in the figure. Which one of the following plots shows the variation of voltage in the coil with time?
1. | ![]() |
2. | ![]() |
3. | ![]() |
4. | ![]() |
A bar magnet is released along the vertical axis of the conducting coil. The acceleration of the bar magnet is:
1. | greater than \(g\). | 2. | less than \(g\). |
3. | equal to \(g\). | 4. | zero. |
A rod having length \(l\) and resistance \(R_0\) is moving with speed \(v\) as shown in the figure. The current through the rod is:
1. \(\frac{B l v}{\frac{R_{1} R_{2}}{R_{1} + R_{2}} + R_{0}}\)
2. \(\frac{Blv}{\left(\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{o}}\right)^{2}}\)
3. \(\frac{B l v}{R_{1} + R_{2} + R_{0}}\)
4. \(\frac{B l v}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{0}}}\)
1. | \(\dfrac{E^{2}}{2 R}\) | 2. | \(\dfrac{E^{2} L}{2 R^{2}}\) |
3. | \(\dfrac{E^{2} L}{R}\) \(\) | 4. | \(\dfrac{E^{2} L}{2 R}\) |
The coefficient of mutual inductance between two coils depends upon:
1. | medium between coils |
2. | separation between coils |
3. | orientation of coils |
4. | All of these |
1. | \(\dfrac{L}{l}\) | 2. | \(\dfrac{l}{L}\) |
3. | \(\dfrac{L^2}{l}\) | 4. | \(\dfrac{l^2}{L}\) |