1.

Four charges equal to −Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium the value of q is

• 
• 
• 
• 

Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surface of spheres A and B is

• 1 : 4

• 4 : 1

• 1:2

• 1:2

A charged particle q is shot towards another charged particle Q which is fixed, with a speed v it approaches Q upto a closest distance r and then returns. If q were given a speed 2v, the closest distances of approach would be

• r

• 2r

• r/2

• r/2

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields , with a velocity perpendicular to both  , and comes out without any change in magnitude or direction of  .Then

Which of the following units denotes the dimensions ML² /Q², where Q denotes the electric charge?

• Weber (Wb)

• Henry (H)

• Wb/m²

• Wb/m²

Two thin wires rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and –q. The potential difference between the centres of the two rings is 

• 
• 

• zero

• zero

Two point charges + 8q and – 2q are located at x = 0 and x = L respectively. The location of a point on the x axis at which the net electric field due to these two point charges is zero is

• 2L

• L/4

• 8L

• 8L

Charges are placed on the vertices of a square as shown. Let E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

•  remains unchanged, V changes 

• Both  and V change

•  and V remain unchanged
•  and V remain unchanged

A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 ≤ r< ∞ , where r is the distance from the centre of the shell? 

A charged ball B hangs from a silk thread S which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to

• cos θ

• cot θ

• sin θ

• sin θ