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#### Question

**(a)** Obtain an expression for the mutual inductance between a long straight wire and a square loop of side *a *as shown in Fig. 6.21.

**(b)** Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, *v *= 10 m/s.

Calculate the induced emf in the loop at the instant when *x *= 0.2 m.

Take *a *= 0.1 m and assume that the loop has a large resistance.

#### Solution

#### Similar questions

A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm s^{−1}in the positive *x-*direction in an environment containing a magnetic field in the positive *z*-direction. The field is neither uniform in space nor constant in time. It has a gradient of 10^{−3} T cm^{−1} along the negative *x-*direction (that is it increases by 10^{− 3} T cm^{−1} as one moves in the negative *x*-direction), and it is decreasing in time at the rate of 10^{−3} T s^{−1}. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50 mΩ.

The current flowing through an inductor of self inductance L is continuously increasing. Plot a graph showing the variation of

Induced emf versus dI/dt

Two cells of emfs *E*_{1} and *E*_{2} and internal resistances *r*_{1} and *r*_{2} are connected in parallel. Derive the expression for the (i) emf and (ii) internal resistance of a single equivalent cell which can replace this combination.

Figure 6.20 shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, *B *= 0.50 T, resistance of the closed loop containing the rod = 9.0 mΩ. Assume the field to be uniform.

**(a) **Suppose K is open and the rod is moved with a speed of 12 cm s^{−1} in the direction shown. Give the polarity and magnitude of the induced emf.

**(b) **Is there an excess charge built up at the ends of the rods when

K is open? What if K is closed?

**(c) **With K open and the rod moving uniformly, there is *no net force *on the electrons in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain.

**(d) **What is the retarding force on the rod when K is closed?

**(e) **How much power is required (by an external agent) to keep the rod moving at the same speed (=12 cm s^{−1}) when K is closed? How much power is required when K is open?

**(f) **How much power is dissipated as heat in the closed circuit?

What is the source of this power?

**(g) **What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular?