A charge Q is placed at the centre of the open end of a cylindrical vessel. The electric flux through the surface of the vessel is:

1. $\frac{\mathrm{q}}{2{\mathrm{\epsilon }}_0}$

2. $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

3. $\frac{2\mathrm{q}}{{\mathrm{\epsilon }}_0}$

4. Zero

A hemispherical surface of radius R is kept in a uniform electric field E as shown in the figure. The flux through the curved surface is:

1. $2{\mathrm{E\pi R}}^2$

2. ${\mathrm{E\pi R}}^2$

3. $4{\mathrm{E\pi R}}^4$

4. Zero

Total electric flux associated with a unit positive charge in a vacuum is:

1. $4{\mathrm{\pi \epsilon }}_0$

2. $\frac{1}{4{\mathrm{\pi \epsilon }}_0}$

3. $\frac{1}{{\mathrm{\epsilon }}_0}$

4. ${\mathrm{\epsilon }}_0$

A charged body has an electric flux F associated with it. Now if the body is placed inside a conducting shell, then the electric flux outside the shell is:

1. Zero

2. Greater than F

3. Less than F

4. Equal to F

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The outward flux over the surface of the cylinder is given by:

1. $2{\mathrm{\pi R}}^2\mathrm{E}$

2. $\frac{{\mathrm{\pi R}}^2\mathrm{E}}{2}$

3. $2\mathrm{\pi RLE}$

4. ${\mathrm{\pi R}}^2\mathrm{E}$

A rectangular surface of sides 10 cm and 15 cm is placed inside a uniform electric field of 25 V/m such that the surface makes an angle of $30°$ with the direction of the electric field. Find the flux of the electric field through the rectangular force.

1. $0.1675 \mathrm{N}/{\mathrm{m}}^2\mathrm{C}$

2. $0.1875 {\mathrm{Nm}}^2/\mathrm{C}$

3. Zero

4. $0.1075 {\mathrm{Nm}}^2/\mathrm{C}$

If an electric field is given by $10\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}$, calculate the electric flux through a surface of area 10 units lying in the yz plane.

1. 100 units

2. 10 units

3. 30 units

4. 40 units

There is a uniform electric field of $8\times {10}^3\hat{\mathrm{i}} \mathrm{N}/\mathrm{C}$. What is the net flux (in SI units) of the uniform electric field through a cube of side 0.3 m oriented so that its faces are parallel to the coordinate plane?

1. $2\times 8\times {10}^3$

2. $0.3\times 8\times {10}^3$

3. Zero

4. $8\times {10}^6\times 6$

A charge Q is kept at the corner of a cube. The electric flux passing through one of those faces not touching that charge is:

1. $\frac{\mathrm{Q}}{24{\mathrm{\epsilon }}_0}$

2. $\frac{\mathrm{Q}}{3{\mathrm{\epsilon }}_0}$

3. $\frac{\mathrm{Q}}{8{\mathrm{\epsilon }}_0}$

4. $\frac{\mathrm{Q}}{6{\mathrm{\epsilon }}_0}$

The electric field in a region is radially outward and at a point is given by $\mathrm{E}=250\mathrm{r} \mathrm{V}/\mathrm{m}$ (where r is the distance of the point from origin). Calculate the charge contained in a sphere of radius 20 cm centred at the origin.

1. $2.22\times {10}^{-6} \mathrm{C}$

2. $2.22\times {10}^{-8} \mathrm{C}$

3. $2.22\times {10}^{-10 }\mathrm{C}$

4. Zero