A conducting rod of length \(2l\) is rotating with constant angular speed \(\omega\) about its perpendicular bisector. A uniform magnetic field \(\vec {B}\) exists parallel to the axis of rotation. The emf induced between the two ends of the rod is:
1. \(B\omega l^2\)
2. \(\frac{1}{2} B \omega l^{2}\)
3. \(\frac{1}{8} B \omega l^{2}\)
4. zero
A conductor ABOCD moves along its bisector with a velocity of \(1\) m/s through a perpendicular magnetic field of \(1~\text{wb/m}^2\), as shown in fig. If all the four sides are of \(1\) m length each, then the induced emf between points A and D is:
1. \(0\)
2. \(1.41\) volt
3. \(0.71\) volt
4. None of the above
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 conducting rod \(AC\) of length \(4l\) is rotated about point \(O\) in a uniform magnetic field \(\vec {B}\) directed into the paper. If \(AO = l\) and \(OC = 3l\), then:
1. \(V_{A} - V_{O} = \dfrac{B \omega l^{2}}{2}\)
2. \(V_{O} - V_{C} = \dfrac{7}{2} B \omega l^{2}\)
3. \(V_{A} - V_{C} = 4 B \omega l^{2}\)
4. \(V_{C} - V_{O} = \dfrac{9}{2} B \omega l^{2}\)
The graph gives the magnitude \(B(t)\) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first:
1. | \(b > (d = e) < (a = c)\) |
2. | \(b > (d = e) > (a = c)\) |
3. | \(b < d < e < c < a\) |
4. | \(b > (a = c) > (d = e)\) |
A square loop of side \(5\) cm enters a magnetic field with \(1\) cms-1. If the front edge enters the magnetic field at \(t=0\), then which graph best depicts emf?
1. | ![]() |
2. | ![]() |
3. | ![]() |
4. | ![]() |
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 |
A coil has \(500\) turns and the flux through the coil is \(\phi=3t^{2} +4t+9\) milliweber. The magnitude of induced emf between the ends of the coil at \(t = 5~\text{s}\) is:
1. \(34\) millivolt
2. \(17\) volt
3. \(17\) millivolt
4. \(34\) volt