One metallic sphere A is given a positive charge whereas another identical metallic sphere B of the exact same mass as of A is given an equal amount of negative charge. Then:

(1) mass of A and mass of B are the same.

(2) mass of A is more.

(3) mass of B is less.

(4) mass of B is more.

Two charges each equal to 2μC are 0.5m apart. If both of them exist inside the vacuum, then the force between them is 

(1) 1.89 N

(2) 2.44 N

(3) 0.144 N

(4) 3.144 N

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

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

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

(4) None of the above

Three charges are placed at the vertices of an equilateral triangle of side ‘a’ as shown in the following figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is 

(1) $Q^2/\left(4\pi {\epsilon }_0{a}^2\right)$

(2) $-Q^2/\left(4\pi {\epsilon }_0{a}^2\right)$

(3) Zero

(4) $Q^2/\left(2\pi {\epsilon }_0{a}^2\right)$

Two particles of equal mass \(m\) and charge \(q\) are placed at a distance of \(16~\text{cm}\). They do not experience any net force. The value of \(\frac{q}{m}\) is: 
1. \(l\)
2. \(\sqrt{\frac{\pi \varepsilon_0}{G}}\)
3. \(\sqrt{\frac{G}{4\pi \varepsilon_0}}\)
4. \(\sqrt{4\pi \varepsilon_0 G}\)

An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius r. The Coulomb force $\overrightarrow{F}$ on 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) $K\frac{e^2}{r^2}\hat{r}$

Five balls numbered \(1\) to \(5\) are suspended using separate threads. Pairs \((1, 2), (2, 4),\) and \((4, 1)\) show electrostatic attraction, while pairs \((2, 3)\) and \((4, 5)\) show repulsion. Therefore ball \((1)\) must be:

1. positively charged
2. negatively charged
3. neutral
4. made of metal

Equal charges q are placed at the four corners A, B, C, D of a square of length a. The magnitude of the force on the charge at B will be 

(1) $\frac{3q^2}{4\pi {\epsilon }_0{a}^2}$

(2) $\frac{4q^2}{4\pi {\epsilon }_0{a}^2}$

(3) $\left(\frac{{\displaystyle 1+2\sqrt{2}}}{{\displaystyle 2}}\right)\frac{q^2}{4\pi {\epsilon }_0{a}^2}$

(4) $\left(2+\frac{{\displaystyle 1}}{{\displaystyle \sqrt{2}}}\right)\frac{q^2}{4\pi {\epsilon }_0{a}^2}$