X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Point A, B, and C are as shown in the figure. Find the incorrect option.

                        

1.  the field at B is $\frac{\mathrm{Q}}{2{\mathrm{\epsilon }}_0\mathrm{A}}$

2.  the field at B is $\frac{\mathrm{Q}}{{\mathrm{\epsilon }}_0\mathrm{A}}$

3.  the fields at A, B and C are of the same magnitude

4.  the fields at A and C are of the same magnitude but in opposite directions

A point charge q is placed at a distance a/2 directly above the centre of a square of side a. The electric flux through the square is:

1. $\frac{q}{{\epsilon }_0}$

2. $\frac{q}{\pi {\epsilon }_0}$

3. $\frac{q}{4{\epsilon }_0}$ 

4. $\frac{q}{6{\epsilon }_0}$

Point charges +4q, –q and +4q are kept on the x-axis at points x = 0, x = a and x = 2a respectively, then 

(1) Only -q is in stable equilibrium

(2) None of the charges are in equilibrium

(3) All the charges are in unstable equilibrium

(4) All the charges are in stable equilibrium

Two-point charges +q and –q are held fixed at (–d, 0) and (d, 0) respectively of a (x, y) coordinate system. Then 

(1) E at all points on the y-axis is along $\hat{i}$

(2) The electric field $\overrightarrow{E}$ at all points on the x-axis has the same direction

(3) Dipole moment is 2qd directed along $\hat{i}$

(4) Work has to be done in bringing a test charge from infinity to the origin

One metallic sphere A is given positive charge whereas another identical metallic sphere B of exactly same mass as of A is given equal amount of negative charge. Then 

(1) Mass of A and mass of B is the same

(2) Mass of A is more

(3) Mass of B is less

(4) Mass of B is more

A point charge q is placed over a horizontal square of side L at a normal distance of L/4 from its centre. Electric flux through the square is 

1. $\mathrm{\varphi }=\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_0}$

2. $\mathrm{\varphi }<\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_0}$

3. $\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_0}<\mathrm{\varphi }<\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

4. $\mathrm{\varphi }>\frac{\mathrm{q}}{6{\mathrm{\epsilon }}_0}$

Consider the charge configuration and spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface, the electric field will be due to:

An electron enters an electric field with its velocity in the direction of the electric lines of force. Then 

(1) The path of the electron will be a circle

(2) The path of the electron will be a parabola

(3) The velocity of the electron will decrease

(4) The velocity of the electron will increase

A point charge of 40 stat coulomb is placed 2 cm in front of an earthed metallic plane plate of large size. Then the force of attraction on the point charge is

(1) 100 dynes

(2) 160 dynes

(3) 1600 dynes

(4) 400 dynes

Two infinitely long parallel wires having linear charge densities λ₁ and λ₂ respectively are placed at a distance of R meters. The force per unit length on either wire will be $\left(K=\frac{{\displaystyle 1}}{{\displaystyle 4\pi {\epsilon }_0}}\right)$

(1) $K\frac{2{\lambda }_1{\lambda }_2}{R^2}$

(2) $K\frac{2{\lambda }_1{\lambda }_2}{R}$

(3) $K\frac{{\lambda }_1{\lambda }_2}{R^2}$ 

(4) $K\frac{{\lambda }_1{\lambda }_2}{R}$