Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity. If the wire AB is replaced by semicircular wire, the magnitude of the induced current will:
1. | increase. |
2. | remain the same. |
3. | decrease. |
4. | increase or decrease depending on whether the semicircle bulges towards the resistance or away from it. |
1. | directly proportional to \(i\). |
2. | directly proportional to \(R\). |
3. | directly proportional to \(R^2\). |
4. | Zero. |
A uniform but time-varying magnetic field \(B(t)\) exists in a circular region of radius \(a\) and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point \(P\) at a distance \(r\) from the centre of the circular region:
1. is zero
2. decreases as \(\frac{1}{r}\)
3. increases as \(r\)
4. decreases as \(\frac{1}{r^2}\)
Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:
1. | maximum in the situation (A). |
2. | maximum in the situation (B). |
3. | maximum in the situation (C). |
4. | the same in all situations. |
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. | ![]() |