A point charge is moving along a straight line with a constant velocity v. Consider a small area A perpendicular to the direction of motion of the charge . Calculate the displacement current through the area when its distance from the charge is x. The value of x is not large so that the electric field at any instant is essentially given by Coulomb's law.

On a frictionless horizontal surface , assumed to be the x-y plane , a small trolley A is moving along a straight line parallel to the y-axis ( see figure) with a constant velocity of (sqrt(3)-1) m//s . At a particular instant , when the line OA makes an angle of 45(@) with the x - axis , a ball is thrown along the surface from the origin O . Its velocity makes an angle phi with the x -axis and it hits the trolley . (a) The motion of the ball is observed from the frame of the trolley . Calculate the angle theta made by the velocity vector of the ball with the x-axis in this frame . (b) Find the speed of the ball with respect to the surface , if phi = (4 theta )//(4) .

A point charge Q is placed at the centre of a spherical conducting shell. A total charge of -q is placed on the shell. The magnitude of the electric field at point P_1 at a distance R_1 from the centre is X. The magnitude of the electric field due to induced charges at point P_2 a distance R_2 from the centre is Y. The values of X and Y are respectively.

A small ball of mass m and charge q is attached to the bottom end of a piece of negligible mass thread of length l, whose top end is fixed. The system formed by the thread and ball is in vertical plane and is in uniform horizontal magnetic field B, which is perpendicular to the plane of figure and points into the paper The ball is started with a velocity v_(0) from lower most point of circle in a direction perpendicular both to the magnetic induction and to direction of thread. The ball moves along a circular path such that thread remains tight during the whole motion. Neglect any loss of enery. What is the magnitude of magnetic induction B, if the minimum initial speed at which the described motion of ball (complete vertical circular motion) occurs is V_(0)=(1)/(2)sqrt(17gL)

A small ball of mass m and charge q is attached to the bottom end of a piece of negligible mass thread of length l, whose top end is fixed. The system formed by the thread and ball is in vertical plane and is in uniform horizontal magnetic field B, which is perpendicular to the plane of figure and points into the paper The ball is started with a velocity v_(0) from lower most point of circle in a direction perpendicular both to the magnetic induction and to direction of thread. The ball moves along a circular path such that thread remains tight during the whole motion. Neglect any loss of enery. By what factor is the force acting on the thread (tension in thread) at point A is greater than at point C, when speed of the ball is the above stated one?

A positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired toward the center of the sphere with velocity v from a point at distance r (r gt R) from the center of the sphere. Find the minimum velocity v so that it can penetrate (R//2) distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

The speed (v) of particle moving along a straight line, when it is of a distance (x) from a fixed point on the line, is given by : v^(2) = 144 - 9x^(2)

Find the direction in which a straight line must be drawn through the point (-1,2) . So that its point of intersection with the line x+y=4 may be at a distance of 3 units from this point.

A charge +Q is fixed at the origin of the co-ordinate system while a small electric dipole of dipolement vecp pointing away from the charge along the x-axis is set free from a point far away from the origin. (a) Calculate the K.E. of the dipole when it reaches to a point (d, 0). (b) Calculate the force on the charge +Q at this moment.

A particle is moving with constant speed v along the line y = a in positive x -direction. Find magnitude of its angular velocity about orgine when its position makes an angle theta with x-axis.

The method of electrical images is used to solve the electrostatic problems, where charge distribution is not specified completely. The method consists of replacement of given charge distribution by a simplified charge distribution or a signal point charge or a number of point charges [rovided the original boundary conditions are still satisfied. For example consider a system consider a system containing a point charge q placed at a distance d of form an infinite conducting plane. The boundary conditions are : (i) Potential is zero at infinity (ii) Potential is zero at each point on the conducting plane If we replaced the conducting plane by a point charge (-q) placed at a distance 'd' opposite to conducting plane. The charge (-q) is called the electrical image. Now system consists of two charge +q an -q at seperation 2d . If charge +q moves to a distance 'y' from the boundary of conducting plane (now absent), the electrical image -q also moves to the same 'y' from the boundary of conducting plane, so that the new distance between +q and -q is 2y The work done in carrying charge q from distance d to distance y from earthed conducting plane is