A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity ω. The induced e.m.f. between the two ends is 

(1) $\frac{1}{2}B\omega l^2$

(2) $\frac{3}{4}B\omega l^2$

(3) $B\omega l^2$

(4) $2B\omega l^2$

Two conducting circular loops of radii \(R_1\) and \(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\), the mutual inductance \(M\) between them will be directly proportional to:

A thin semicircular conducting ring of radius \(R\) is falling with its plane vertical in a horizontal magnetic induction \(B\). At the position \(MNQ\), the speed of the ring is \(v\) and the potential difference developed across the ring is:

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

A circular loop of radius R carrying current I lies in the x-y plane with its centre at the origin. The total magnetic flux through the x-y plane is 

(1) Directly proportional to I

(2) Directly proportional to R

(3) Directly proportional to R²

(4) Zero

A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to 

(1) l / L

(2) l² / L

(3) L/l

(4) L²/l

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 $\frac{1}{r^2}$

A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0 so that a time-dependent current I₁(t) starts flowing through the coil. If I₂(t) is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to I₁(t), then as a function of time (t > 0), the product I₂ (t) B(t) 

(1) Increases with time

(2) Decreases with time

(3) Does not vary with time

(4) Passes through a maximum

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be 

(1) Maximum in situation (A)

(2) Maximum in situation (B)

(3) Maximum in 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 $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is 

(1) BΩl²

(2) $\frac{1}{2}B\omega l^2$

(3) $\frac{1}{8}B\omega l^2$

(4) Zero