The electric field in a region is given by $$\overrightarrow{E}=\left(Ax+B\right)\stackrel{\wedge }{i}$$ , where E is in NC–1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V1 and that at x = –5 is V2, then V1 – V2 is :-

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –4 Q, the new potential difference between the same two surfaces is :

The bob of a simple pendulum has mass 2g and a charge of 5.0 μC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is : (take g = 10 m/s2)

Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :

Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :

Two point charges q1$$\left(\sqrt{10}\mu C\right)$$ and q2($$-$$ 25 $$\mu$$C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, [take {1 \over {4\pi { \in _0}}} = 9 $$\times$$ 109 Nm2C$$-$$2]

Charge is distributed within a sphere of radius R with a volume charge density \rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}}, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -

Two electric dipoles, A, B with respective dipole moments $${\overrightarrow{d}}_A=-4qai$$ and $${\overrightarrow{d}}_B=-2qai$$ are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is -

Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that OP' = \left( {{y \over 3}} \right), the force on Q will be close to - \left( {{y \over 3} > > 2a} \right)

Three charges Q, + q and + q are placed at the vertices of a right-angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is :

The given graph shows variation (with distance r form centre) of :

An electric field of 1000 V/m is applied to an electric dipole at angle of 45o. The value of electric dipole moment is 10–29 C.m. What is the potential energy of the electric dipole?

There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R (t) is :

Ship A is sailing towards north-east with velocity $$\overrightarrow{v}=30\stackrel{\wedge }{i}+50\stackrel{\wedge }{j}$$ km/hr where $$\stackrel{\wedge }{i}$$ points east and $$\stackrel{\wedge }{j}$$ , north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will be at minimum distance from B in :

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct ?

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2 . If it were launched at an angle $$\theta$$0 with speed v0 then (g = 10 ms–2) :

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the product t1t2 is -

A plane is inclined at an angle $$\alpha$$ = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms–1 , from the base of the plane, making an angle $$\theta$$ = 15° with respect to the plane as shown in the figure. the distance from the base, at which the particle hits the plane is close to : (Take g = 10 ms –2)