Gauss's Law

Q.

Gauss’s law is defined and valid only for a closed surface.

1. True

2. false

Q. The inward and outward electric flux for a closed surface in units of $N-m^2/c$ are respectively $8\times {10}^3$ and $4\times {10}^3$. Then the total charge inside the surface is [where $ϵ$ = permittivity constant]

1. -4 X 10³ C
2. 
3. 
4. 4 X 10³ C

Q.

1. 
   

2. Zero

3. 
   

4. 
   

Q.

Comment on the correctness of the following two statements:

Statement I => Gauss’s law is valid only for symmetrical Gaussian surfaces with respect to the charge distribution.

Statement II => Gauss’s law is valid only for charges placed in vacuum.

1. True, True

2. True, false

3. False, True

4. False, False

Q.

The electric flux through the surface S as due to all the charges as shown in following figure is$\frac{q_1+q_3-q_2-q_4}{{ϵ}_0}$

1. True

2. false

Q. Electric charge is uniformly distributed alone 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. $\frac{Q}{{ϵ}_0}$
2. $\frac{100Q}{\left(\pi {ϵ}_0\right)}$
3. $\frac{100Q}{{ϵ}_0}$
4. $\frac{10Q}{\left(\pi {ϵ}_0\right)}$

Q.

A spherical volume contains a uniformly distributed charge of volume density $2.0\times {10}^{-4}C{m}^{-3}$. Find the strength of electric field at a point inside the volume at a distance $4.0cm$ from the centre.

1. $3\times {10}^4\frac{N}{C}$

2. $3\times {10}^5\frac{N}{C}$

3. $3\times {10}^6\frac{N}{C}$

4. $3\times {10}^7\frac{N}{C}$

Q.

A long string with charge per unit length λ on it passes through a cube of side a. The minimum and maximum flux through the cube will be

1. 
2. 
3. 
4. 

Q.

The figure shows an imaginary cube of length L/2 and a uniformly charged rod of length L touching the centre of the right face of the cube normally. At time t=0, the rod starts moving to the left slowly at a constant speed v. the electric flux(F) through the cube is plotted against time(t). the correct graph showing the variation of flux with time is

1. 
2. 
3. 
4. 

Q.

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. 
2. 
3. 
4.