An electric dipole is put in north-south direction in a sphere filled with water. Which statement is correct ?

(1) Electric flux is coming towards sphere

(2) Electric flux is coming out of sphere

(3) Electric flux entering into sphere and leaving the sphere are same

(4) Water does not permit electric flux to enter into sphere

The electric flux for Gaussian surface A that encloses the charged particles in free space is (given q₁ = –14 nC, q₂ = 78.85 nC, q₃ = – 56 nC) 

(1) 10³ Nm² C^–1

(2) 10³ CN^-1 m^–2

(3) 6.32 × 10³ Nm² C^–1

(4) 6.32 × 10³ CN^-1 m^–2

The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a distance r(r > R) from its axis is 

(1) Directly proportional to r²

(2) Directly proportional to r³

(3) Inversely proportional to r

(4) Inversely proportional to r²

An electrostatic line of force in the xy plane is given by equation x² + y² = 1. A particle with unit positive charge, initially at rest at the point x = 1, y = 0 in the xy plane will -

1. Not move at all

2. Will move along straight line

3. Will move along the circular line of force

4. The data given in the question is contradictory

A positively charged ball hangs from a silk thread. We put a positive test charge q₀ at a point and measure F/q₀, then it can be predicted that the electric field strength E 

(1) > F/q₀

(2) = F/q₀

(3) < F/q₀

(4) Cannot be estimated

A solid metallic sphere has a charge +3Q. Concentric with this sphere is a conducting spherical shell having charge –Q. The radius of the sphere is a and that of the spherical shell is b (b > a). What is the electric field at a distance R(a < R < b) from the centre 

(1) $\frac{Q}{2\pi {\epsilon }_{0}R}$

(2) $\frac{3Q}{2\pi {\epsilon }_{0}R}$

(3) $\frac{3Q}{4\pi {\epsilon }_0{R}^2}$

(4) $\frac{4Q}{4\pi {\epsilon }_0{R}^2}$ 

A point charge \(q\) is placed at a distance \(\frac{a}{2}\) directly above the centre of a square of side \(a\). The electric flux through the square (i.e. one face) is:
1. \(\frac{q}{\varepsilon_0}\)
2. \(\frac{q}{\pi\varepsilon_0}\)
3. \(\frac{q}{4\varepsilon_0}\)
4. \(\frac{q}{6\varepsilon_0}\)

Two infinitely long parallel wires having linear charge densities λ₁ and λ₂ respectively are placed at a distance of R meters. The force per unit length on either wire will be $\left(K=\frac{{\displaystyle 1}}{{\displaystyle 4\pi {\epsilon }_0}}\right)$

(1) $K\frac{2{\lambda }_1{\lambda }_2}{R^2}$

(2) $K\frac{2{\lambda }_1{\lambda }_2}{R}$

(3) $K\frac{{\lambda }_1{\lambda }_2}{R^2}$ 

(4) $K\frac{{\lambda }_1{\lambda }_2}{R}$

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