A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will

1.  be reduced to half

2.  remain the same

3.  be doubled

4.  increased four times

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow{\mathrm{E}}$. Due to the force q$\overrightarrow{\mathrm{E}}$, its velocity increases from 0 to 6 m/s in one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively:-

1. 2 m/s, 4 m/s

2. 1 m/s, 3 m/s

3. 1 m/s, 3.5 m/s

4. 1.5 m/s, 3 m/s

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.