Electric Charges and Fields

Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as

1. v x-1/2
2. v x-1
3. v x1/2
4. v x

An electric dipole is placed at an angle of 30 with an electric field intensity 2 105 N C-1. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is

1. 8 mC
2. 2 mC
3. 5 mC
4. 7

The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by

1. 4 0 Aa3
2. 0 Aa3
3. 4 0 Aa2
4. A 0 a2

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes [figure]

1. ( 2r 3 )
2. ( 2r3 )
3. ( 1 2 )2 r
4. ( r [3]2 )

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to

1. -Q/4
2. Q/4
3. -Q/2
4. Q/2

What is the flux through a cube of side a if a point charge of q is at one of its corners?

1. 2q 0
2. q8 0
3. q 0
4. q2 06a2

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will

1. increase four times
2. be reduced to half
3. remain the same
4. be doubled

The electric field at a distance 3R2 from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance R2 from the centre of the sphere is

1. zero
2. E
3. E2
4. E3

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

1. 4 0 F d2e2
2. 4 0 F e2d2
3. 4 0 F d2e2
4. 4 0 F d2q2

A square surface of side L meter in the plane of the paper is placed in a uniform electric field E (volt/m) acting along the same plane at an angle with the horizontal side of the square as shown in figure. [figure] The electric flux linked to the surface, in units of volt m is

1. EL2
2. EL2
3. EL2
4. zero