Electric Charges and Fields

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

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is [figure]

1. E along KO
2. 3E along OK
3. 3E along KO
4. E along OK

A hollow cylinder has a charge q coulomb within it. If is the electric flux in units of volt-metre associated with the curved surface B, the flux linked with the plane surface A in units of V-m will be [figure]

1. q2 0
2. 3
3. q 0 -
4. 12 ( q 0 - )

Three point charges +q, -2q and + q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

1. 2qa along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)
2. qa along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)
3. 2qa along +x direction
4. 2qa along +y direction