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. \(Q^{2} / \left(\right. 4 \pi \epsilon_{0} a^{2} \left.\right)\)

2. \(- Q^{2} / \left(\right. 4 \pi \epsilon_{0} a^{2} \left.\right)\)

3. zero

4. \(Q^{2} / \left(\right. 2 \pi \epsilon_{0} a^{2} \left.\right)\)

Two particles of equal mass m and charge q are placed at a distance of 16 cm. They do not experience any force. The value of $\frac{q}{m}$ is 

(1) l

(2) $\sqrt{\frac{\pi {\epsilon }_0}{G}}$

(3) $\sqrt{\frac{G}{4\pi {\epsilon }_0}}$

(4) $\sqrt{4\pi {\epsilon }_{0}G}$

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

1. zero.

2. greater than in copper.

3. equal to that in copper.

4. less than in copper.

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

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

(2) $\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$

(3) Zero

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

A charge particle is free to move in an electric field. It will travel 

(1) Always along a line of force

(2) Along a line of force, if its initial velocity is zero

(3) Along a line of force, if it has some initial velocity in the direction of an acute angle with the line of force

(4) None of the above

An uncharged sphere of metal is placed in between two charged plates as shown. The lines of force look like 

(1) A

(2) B

(3) C

(4) D

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

The dimension of (1/2) ${\epsilon }_0{E}^2 ({\epsilon }_0$: permittivity of free space; E: electric field) is

(1) MLT^–1

(2) ML²L^–2

(3) ML^–1T^–2

(4) ML²T^–1

An electron having charge ‘e’ and mass ‘m’ is moving in a uniform electric field E. Its acceleration will be 

(1) $\frac{e^2}{m}$

(2) $\frac{E^{2}e}{m}$

(3) $\frac{eE}{m}$

(4) $\frac{mE}{e}$

A pendulum bob of mass $30.7\times {10}^{-6}kg$ and carrying a charge $2\times {10}^{-8}C$ is at rest in a horizontal uniform electric field of 20000 V/m. The tension in the thread of the pendulum is $(g=9.8m/s^2)$

(1) $3\times {10}^{-4}N$

(2) $4\times {10}^{-4}N$

(3) $5\times {10}^{-4}N$

(4) $6\times {10}^{-4}N$