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

Two identical conductors of copper and aluminium are placed in an identical electric field. The magnitude of induced charge in the aluminum will be 

(1) Zero

(2) Greater than in copper

(3) Equal to that in copper

(4) Less than in copper

Two spherical conductors \(B\) and \(C\) having equal radii and carrying equal charges in them repel each other with a force \(F\) when kept apart at some distance. A third spherical conductor having same radius as that of \(B\) but uncharged is brought in contact with \(B\), then brought in contact with \(C\) and finally removed away from both. The new force of repulsion between \(B\) and \(C\) is:
1. \(\frac{F}{4}\)
2. \(3\frac{F}{4}\)
3. \(\frac{F}{8}\)
4. \(3\frac{F}{8}\)

Two equally charged, identical metal spheres A and B repel each other with a force 'F'. The spheres are kept fixed with a distance 'r' between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is 

(1) F

(2) 3F/4

(3) F/2

(4) F/4

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium, if q is equal to 

(1) $-\frac{Q}{2}$

(2) $-\frac{Q}{4}$

(3) $+\frac{Q}{4}$

(4) $+\frac{Q}{2}$ 

The figure shows the electric lines of force emerging from a charged body. If the electric fields at A and B are E_A and E_B respectively and if the distance between A and B is r, then:

1. \(E_{A}~>~E _{B}\)
2. \(E_{A}~<~E _{B}\)
3. \(E_{A}~=~\frac{E_{B}}{r^{}}\)
4. \(E_{A}~=~\frac{E_{B}}{r^{2}}\)

\(ABC\) is an equilateral triangle. Charges \(+q\)  are placed at each corner. The electric intensity at \(O\) will be: