In the figure, two positive charges q₂ and q₃ fixed along the y-axis, exert a net electric force in the +x-direction on a charge q₁ fixed along the x-axis. If a positive charge Q is added at (x, 0), the force on q₁

1. shall increase along the positive x-axis.

2. shall decrease along the positive x-axis.

3. shall point along the negative x-axis.

4. shall increase but the direction changes because of the intersection of Q with q₂ and q₃.

A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by:

1.                        2.

3.                   4. 

The electric flux through the surface

(1) in Fig. (iv) is the largest

(2) in Fig. (iii) is the least

(3) in Fig. (ii) is same as Fig. (iii) but is smaller than Fig. (iv)

(4) is the same for all the figures

Five charges q₁, q₂, q₃, q₄, and q₅ are fixed at their positions as shown in the figure, S is a Gaussian surface. The Gauss' law is given by ${\int }_{\mathbf{S}}\mathbf{E}.\mathrm{d}\mathbf{S}=\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$. Which of the following statements is correct?

1. E on the LHS of the above equation will have contribution from q₁, q₅ and q₃ while q on the RHS will have a contribution from q₂ and q₄ only.

2. E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q₂ and q₄ only.

3. E on the LHS of the above equation will have a contribution from all charges while q on the RHS will have a contribution from q₁, q₃ and q₅ only.

4. Both E on the LHS and q on the RHS will have contributions from q₂ and q₄ only.

The figure shows electric field lines in which an electric dipole p is placed as shown. Which of the following statements is correct?
                      
1. The dipole will not experience any force.

2. The dipole will experience a force towards the right.

3. The dipole will experience a force towards the left.

4. The dipole will experience a force upwards.

A point charge +q is placed at a distance d from an isolated conducting plane. The field at a point P on the other side of the plane is:

1. directed perpendicular to the plane and away from the plane.

2. directed perpendicular to the plane but towards the plane.

3. directed radially away from the point charge.

4. directed radially towards the point charge.

A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed:

1. perpendicular to the diameter.

2. parallel to the diameter.

3. at an angle tilted towards the diameter.

4. at an angle tilted away from the diameter.

If ${\int }_{\mathbf{S}}\mathbf{E}.\mathrm{d}\mathbf{S}=0$ over a surface, then

(a) the electric field inside the surface and on it is zero.

(b) the electric field inside the surface is necessarily uniform.

(c) the number of flux lines entering the surface must be equal to the number of flux lines leaving it.

(d) all charges must necessarily be outside the surface.

1. (a, c)

2. (b, c)

3. (c, d)

4. (a, d)

The electric field at a point is:

(a) always continuous

(b) continuous if there is no charge at that point

(c) discontinuous only if there is a negative charge at that point

(d) discontinuous if there is a charge at that point

1. (a, b)

2. (b, d)

3. (c, d)

4. (a, d)

If there were only one type of charge in the universe, then,