A charge q is placed at the centre of the open end of the cylindrical vessel. The flux of the electric field through the surface of the vessel is 

(1) Zero

(2) $\frac{q}{{\epsilon }_0}$

(3) $\frac{q}{2{\epsilon }_0}$

(4) $\frac{2q}{{\epsilon }_0}$ 

Electric charge is uniformly distributed along a long straight wire of radius \(1\) mm. The charge per cm length of the wire is \(Q\) coulomb. Another cylindrical surface of radius \(50\) cm and length \(1\) m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is:

      
1. \(\frac{Q}{\varepsilon _{0}}\)

2. \(\frac{100Q}{\varepsilon _{0}}\)

3. \(\frac{10Q}{\pi\varepsilon _{0}}\)

4. \(\frac{100Q}{\pi\varepsilon _{0}}\)

The S.I. unit of electric flux is 

(1) Weber

(2) Newton per coulomb

(3) Volt × metre

(4) Joule per coulomb

Shown below is a distribution of charges. The flux of electric field due to these charges through the surface S is 

(1) $3q/{\epsilon }_0$

(2) $2q/{\epsilon }_0$

(3) $q/{\epsilon }_0$ 

(4) Zero

Consider the charge configuration and spherical Gaussian surface as shown in the figure. While calculating the flux of the electric field over the spherical surface, the electric field will be due to: 

(1) q₂ only

(2) Only the positive charges

(3) All the charges

(4) +q₁ and – q₁ only

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

Two equal negative charges of charge – q are fixed at the points (0, a) and (0, –a) on the Y-axis. A positive charge Q is released from rest at the point (2a, 0) on the X-axis. The charge Q will:

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