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A particle having charge ${\mathrm{q}}_1$ exerts F electrostatic force on charge ${\mathrm{q}}_2$ at rest. If a particle having charge $\frac{q_1}{4}$ is placed midway between the line joining the two charges ${\mathrm{q}}_1 \mathrm{and} {\mathrm{q}}_2$ then electrostatic force on ${\mathrm{q}}_2$ due to ${\mathrm{q}}_1$ will become/remain
1. 2F
2. $\frac{F}{2}$
3. F
4. zero
 

An electric dipole of dipole moment p is placed in an electric field of intensity E such that angle between electric field and dipole moment is $\theta$. Assuming that the potential energy of the dipole is zero when $\theta =0°$, the potential energy of the dipole will be
1. -pE cos$\theta$
2. pE(1-cos$\theta$)
3. pE(cos$\theta$-1)
4. -2pE(cos$\theta$-1)

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

Four charges are arranged at the corners of a square \(ABCD,\) as shown in the adjoining figure. The force on the positive charge \(Q\) kept at the centre \(O\) is:
       

Three charges \(4q,Q,\) and \(q\) are in a straight line in the position of \(0,l/2,\) and \(l\) respectively. The resultant force on \(q\) will be zero if \(Q\) equal to:
1. \(-q\)
2. \(-2q\)
3. \(\frac{-q}{2}\)
4. \(4q\)

Two charges \(+2\) C and \(+6\) C are repelling each other with a force of \(12\) N. If each charge is given \(-2\) C of charge, then the value of the force will be:

Force of attraction between two point charges Q and – Q separated by d meter is F_e. When these charges are given to 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. 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) $Q^2/\left(2\pi {\epsilon }_0{a}^2\right)$

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 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

The magnitude of electric field intensity E is such that, an electron placed in it would experience an electrical force equal to its weight is given by 
(1) mge
(2) $\frac{mg}{e}$
(3) $\frac{e}{mg}$
(4) $\frac{e^2}{m^2}g$

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.

The figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero?


(1) 1
(2) 2
(3) 3
(4) 4

Two small spherical balls each carrying a charge Q = 10 μC (10 micro-coulomb) are suspended by two insulating threads of equal lengths 1m each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle 60° between them, as shown in the figure. What is the tension in the threads (Given: $\frac{1}{\left(4\pi {\epsilon }_0\right)}=9\times {10}^{9}Nm/C^2$) 

(1) 18 N
(2) 1.8 N
(3) 0.18 N
(4) None of the above

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) $6\times {10}^{-4}N$ 

A charged ball \(B\) hangs from a silk thread \(S,\) which makes an angle \(\theta\) with a large charged conducting sheet \(P,\) as shown in the figure. The surface charge density \(\sigma\) of the sheet is proportional to: 
               
1. \(\sin\theta\)
 2. \(\tan\theta\)
 3. \(\cos\theta\)
 4. \(\cot\theta\)

The charge on 500 cc of water due to protons will be:
1. 6.0 × 10²⁷ C
2. 2.67 × 10⁷ C
3. 6 × 10²³ C
4. 1.67 × 10²³ C