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 circular loop of radius R, carrying current I, lies n XY-plane with its centre at origin. The total magnetic flux through XY-plane is

A circular brass loop of radius a and resistance R is placed with its plane perpendicular to the magnetic field which varies with time as B=B_0 sin omegat . Obtain an expression for the induced current in the loop.

Two identical circular wires P and Q each of radius R and carrying current 'I' are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.

A small magnet of magnetic moment pixx10^(-3) Am^(2) is placed on the Y-axis at a distance of 0.1 from the origin with its axis parallel to the X-axix. A coil have 169 turns and radius 0.05 m is placed on the X-axis at a distance of 0.12 m from the origin with the axis of the coil coinciding with the X-axis. Find the magnitude and direction of the current in the coil for a compass needle placed at the origin, to point in the north-south direction.

A rectangular coil of N turns and ara of cross-section A is held in a time-varying field given by B = B_0 cosomegat , with the plane of the coil noral to the magnetic field. Deduce an expression for the e.m.f. induced in the coil.

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 wire loop carrying a current I is placed in the xy-plane as shown in figure If an external uniform magnetic induction field B=Bhati is applied, find the force acting on the loop due to this field.