Electric Charges and Fields

An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field $200\frac{N}{C}$ as shown in the figure. A body of mass 1kg and charge 5 mC is allowed to slide down from rest at a height of 1m. If the coefficient of friction is 0.2, find the time taken by the body to reach the bottom.

$\left[g=9.8m/s^2;sin30°=\frac{1}{2};cos30°=\frac{\sqrt[]{3}}{2}\right]$

A uniform electric field E = (8m/e) V/m is created between two parallel plate of length 1m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation ( θ) of the path of the electron as it comes out of the field will be________.

The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side ‘a’ as shown in figure. The magnitude of electric field (E) at the corner D of the square, is

Given below are two statements:

Statement – I : A point change is brought in an electric field. The value of electric field at a point near to the change may increase if the charge is positive.

Statement – I : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.

Choose the correct answer from the options given below:

A spherically symmetric charge distribution is considered with charge density varying

as $\rho \left(r\right)=\{\begin{array}{cc}\hfill {\rho }_0\left(\frac{3}{4}-\frac{r}{R}\right)for\hfill & \hfill r\le R\hfill \\ \hfill zero\hfill & \hfill forr>R\hfill \end{array}$

Where, r(r < R) is the distance from the centre O (as shown in figure). The electric field at point P will be:

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1 m. The ratio of net force on a charged ball to the force between any two charged balls will be

If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be:

A positive charge Qis uniformly distributed along a circular ring of radius R. A small test charge q is placed at the centre of the ring as shown in figure. Then

(a) If q>0 and is displaced away from the centre in the plane of the ring it will be pushed back towards the centre

(b) If q<0 and is displaced away from the centre in the plane of the ring, it will never return to the centre an will continue moving till it hits the ring

(c) If q<0 , it will perform SHM for small displacement along the axis.

(d) Q at the centre of the ring is in an unstable equilibrium within the plalne of the ring for q>O

A positive charge Q is uniformly distributed along a circular ring of radius R. A small test charge q is placed at the centre of the ring figure. Then,

(a) If q > 0 and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre

(b) If q < 0 and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring

(c) If q < 0, it will perform SHM for small displacement along the axis

(d) Q at the centre of the ring is in an unstable equilibrium within the plane of the ring for q > 0

Refer to the arrangement of arrangement of charges in figure and a gaussian surface of radius R with Q charge at the center. Then 

(a) Total flux through the surface of the sphere is $\frac{-Q}{\mathit{\epsilon }0}$ .

(b) Field on the surface of the sphere of the sphere is -Q/4 $\pi \epsilon$ ₀R².

(c) Flux through the surface of sphere due to 5Q is zero.

(d) Field on the surface of sphere due to -2Q is same everywhere