A long solenoid has n turns per unit length and radius a. A current `I = I _ 0 sin omega` t flows through it. A cylindrical vessel of radius R, length L, thickness d `(d lt lt R)` and
resistivity `rho` is kept coaxially shown int he figure. Find the induced current in the outer cylindrical vessel. `
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A magnetic field in a certain region is given by bar B = B_0 cos omegathatk and a coil of radius a with resistanc R is placed i the XY-plane with its centre at the origin in the magnetic field as shown in the figure. Find the magnitude and direction of current at (a,0,0) at t = pi//2 omega

A metal bar AB can slide on two parallel thick metallic rails separated by a distance l. A resistance R and an inductance L are connected to the rails as shown in the figure. A long straight wire carrying a constant current I_(0) is placed in the plane of the rails and perpendicular to them as shown. The bar AB is held at rest at a distance x_(0) from the long wire. At t=0, it is made to slide on the rails away from wire. Answer the following questions. Find a relation among i, (di)/(dt) and (d phi)/(dt) , where i is the current in the circuit and phi is the flux of the megnetic field due to the long wire through the circuit.

A current I=3.36 (1+2t)xx 10^-2 A increases at a steady rate in a long straight wire. A small circular loop of radius 10^-3 m has its plane parallel to the wire and is at a placed at a distance of 1 m from the wire. The resistance of the loop is 8.4 xx 10^-4 Omega . find the megnitude and the direction of the induced current in the loop.

A right circular cylinder of length L (in m) and of radius R (in m) has its center at the origin and its length along the X-axis. A uniform electric field vecE = E_x hat I N C^-1 for x > 0 and vec E = -E_xhati NC^-1 for x < 0 exists over the cylinder. Find the net charge enclosed by the cylinder.

A rectangular loop has a sliding connector PQ of length l and resistance R. It is moving with a speed v as shown in the figure. The set up is placed in a uniform magnetic field goping into the plane of the paper. The three currents I_1 , I_2 and I are

A magnetic filed vecB=B_0 sin"(omega t)hatk covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d (Fig. EP 6.22). The wires are in the x-y plane. The wire AB (of length d) has resistance R and parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit? what is the force needed to keep the wire moving at constant velocity?

A right circular cylinder of length L (in m) and of radius R (in m) has its center at the origin and its length along the X-axis. A uniform electric field vecE = E_x hat I N C^-1 for x > 0 and vec E = -E_xhati NC^-1 for x < 0 exists over the cylinder. Find net outward electric flux

Figure shows a short solenoid of length 4 cm, radius 2.0 cm and number of turns 100., lying inside on the axis of a long solenoid, 80 cm long and number of turns 1,500. What is the flux through the long solenoid, if a current of 5.0 A flows through the short solenoid? Also obtain the mutual inductance of the two solenoids.