A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre:

1. decreases as r increases for r < R and for r > R

2. increases as r increases for r < R and for r > R

3. zero as r increases for r < R, decreases as r increases for r > R

4. zero as r increases for r < R, increases as r increases for r > R

Three-point charges + q and -2q and +q are placed at points (x=0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x= a, y = 0, z = 0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:

1. $\sqrt{2}$qa along + y direction

2. $\sqrt{2}$qa along the line joining points (x=0, y= 0, z= 0) and (x=a, y=a, z=0)

3. qa along the line joining points (x= 0, y=0, z=0) and (x=a, y=a, z=0)

4. $\sqrt{2}$qa along + x direction

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

The dielectric constant of pure water is 81. Its permittivity will be 

(1) 7.17 × 10^–10 MKS units

(2) 8.86 × 10^–12 MKS units

(3) 1.02 × 10¹³ MKS units

(4) Cannot be calculated

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) $\frac{2q}{{\epsilon }_0}$ 

There is a uniform electric field of strength 10³ V/m along the y-axis. A body of mass 1g and charge 10^–6C is projected into the field from the origin along the positive x-axis with a velocity 10m/s. Its speed in m/s after 10s is (Neglect gravitation) 

(1) 10

(2) $5\sqrt{2}$

(3) $10\sqrt{2}$

(4) 20

Four-point +ve charges of the same magnitude (Q) are placed at four corners of a rigid square frame as shown in the figure. The plane of the frame is perpendicular to Z-axis. If a –ve point charge is placed at a distance z away from the above frame (z<<L) then 

(1) – ve charge oscillates along the Z-axis.

(2) It moves away from the frame

(3) It moves slowly towards the frame and stays in the plane of the frame

(4) It passes through the frame only once.

X and Y are large, parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Point A, B, and C are as shown in the figure. Find the incorrect option.

1.  the field at B is $\frac{\mathrm{Q}}{2{\mathrm{\epsilon }}_0\mathrm{A}}$

2.  the field at B is $\frac{\mathrm{Q}}{{\mathrm{\epsilon }}_0\mathrm{A}}$

3.  the fields at A, B and C are of the same magnitude

4.  the fields at A and C are of the same magnitude but in opposite directions

A point charge q is placed at a distance a/2 directly above the centre of a square of side a. The electric flux through the square is:

1. $\frac{q}{{\epsilon }_0}$

2. $\frac{q}{\pi {\epsilon }_0}$

3. $\frac{q}{4{\epsilon }_0}$ 

4. $\frac{q}{6{\epsilon }_0}$