A line charge `lambda` per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Fig. 6.22). A uniform magnetic field extends over a circular region within the rim. It is given by, `B = -B_0k` `(r oversetlarr a, a < R)` = 0 (otherwise) What is the angular velocity of the wheel after the field is suddenly switched off? :

A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y-axis (see figure). Take the vertically upward direction as the z-axis. A uniform magnetic field vec(B) = (3 hat(i) + 4hat(k)) B_(0) exists in the region. The loop is held in the x-y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium What is the direction of the current I in PQ?

A circular ring of radius R with uniform positive charge density lambda per unit length is located in the y z plane with its center at the origin O. A particle of mass m and positive charge q is projected from that point p( - sqrt(3) R, 0,0) on the negative x - axis directly toward O, with initial speed V. Find the smallest (nonzero) value of the speed such that the particle does not return to P ?

A magnetic field vecB is confined to a region r le a and points out of the paper (the z axis), r = 0 being the centre of the circular region. A charged ring (charge = Q) of radius b, b>a and mass m lies in the x-y plane with its centre at the origin. The ring is free to rotate and is at rest. the magnetic field is brought to zero in time Deltat . Find the angular velocity omega of the ring after the field vanishes.

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.

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, B= (mu_0IR^2N)/(2(x^2+R^2)^(3/2)) . Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to R, and is given by, B=0.72 (mu_0NI)/R approximately.