A hollow cylinder has a charge q coulomb within it(at the geometrical centre). If ϕ is the electric flux in unit of voltmeter associated with the curved surface B, the flux linked with the plane surface A in unit of voltmeter will be: 

1. $\frac{1}{2}\left(\frac{q}{{\epsilon }_0}-\Phi \right)$

2. $\frac{q}{2{\epsilon }_0}$

3. $\frac{\Phi }{3}$

4. $\frac{q}{{\epsilon }_0}-\Phi$

A square surface of side L metre in the plane of the paper is placed in a uniform electric field E (volt/m) acting along the same place at an angle θ with the horizontal side of the square as shown in figure. The electric flux linked to the surface in unit of V-m, is 

1. $E{L}^2$

2. $E{L}^2 \cos \theta$

3. $E{L}^2 \sin \theta$

4. 0

An electron falls from rest through a vertical distance h in a uniform and vertically upward-directed electric field E. The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in through the same vertical distance h. The time fall of the electron, in comparison to the time fall of the proton is :-

1. smaller

2. 5 times greater

3. 10 times greater

4. equal

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