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
2:1
D.
2:1
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
4L
A.
2L
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
tan θ
D.
tan θ
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
Both and V change
D.
changes, V remains unchangedA 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.
Which of the following units denotes the dimensions ML^{2} /Q^{2}, where Q denotes the electric charge?
Weber (Wb)
Henry (H)
Wb/m^{2}
H/m^{2}
B.
Henry (H)
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
A.
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
B.
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/4
D.
r/4
By principle of conservation of energy
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
B.