A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius b and outer radius c is concentric with the solid sphere and has a net charge –Q. The surface charge density on the inner and outer surfaces of the spherical shell will be 

(1) $-\frac{2Q}{4\pi b^2},\frac{Q}{4\pi c^2}$

(2) $-\frac{Q}{4\pi b^2},\frac{Q}{4\pi c^2}$

(3) $0,\frac{Q}{4\pi c^2}$

(4) None of the above

Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when 

(1) $x=\frac{d}{\sqrt{2}}$

(2) $x=\frac{d}{2}$

(3) $x=\frac{d}{2\sqrt{2}}$

(4) $x=\frac{d}{2\sqrt{3}}$

An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The Coulomb force $\overrightarrow{F}$ on the electron is: (Where $K=\frac{1}{4\pi {\epsilon }_0}$) 
1. $-K\frac{e^2}{r^3}\hat{r}$
2. $K\frac{e^2}{r^3}\overrightarrow{r}$
3. $-K\frac{e^2}{r^3}\overrightarrow{r}$
4. $K\frac{e^2}{r^2}\hat{r}$

F_g and F_e represents gravitational and electrostatic force respectively between electrons situated at a distance 10 cm. The ratio of F_g/ F_e is of the order of 

(1) 10⁴²

(2) 10

(3) 1

(4) 10^–43

Force of attraction between two point charges Q and – Q separated by d meter is F_e. When these charges are placed on two identical spheres of radius R = 0.3 d whose centres are d meter apart, the force of attraction between them is 

(1) Greater than F_e

(2) Equal to F_e

(3) Less than F_e

(4) Less than F_e

If a soap bubble is given some charge, then its radius

(1) Increases

(2) Decreases

(3) Remain unchanged

(4) May increase or decrease depending upon the give charge is positive or negative

Three infinitely long charge sheets are placed as shown in the figure. The electric field at point \(P\) is:

The electric field in a certain region is acting radially outward and is given by E=Ar. A charge contained in a sphere of radius 'a' centered at the origin of the field will be given by

1. $4\pi {\in }_{o}A{a}^2$

2. $\pi {\in }_{o}A{a}^2$

3. $4\pi {\in }_{o}A{a}^3$

4. ${\in }_{o}A{a}^2$

Infinite charges of magnitude q each are lying at x =1, 2, 4, 8... meter on X-axis. The value of the intensity of the electric field at point x = 0 due to these charges will be 

(1) 12 × 10⁹q N/C

(2) Zero

(3) 6 × 10⁹q N/C

(4) 4 × 10⁹q N/C

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

1. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2 }{e^2}$                  2. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fe}}^2}{d^2}}$

3. $\sqrt{\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{e^2}}$               4. $\frac{4{\mathrm{\pi \epsilon }}_{\circ }{\mathrm{Fd}}^2}{q^2}$