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

An isolated solid metal sphere of radius R is given an electric charge. Which of the graphs below best shows the way in which the electric field E varies with distance x from the centre of the sphere?

1. 

2. 

3. 

4. 

The electric field intensity at P and Q in the shown arrangement are in the ratio of:

1. 1: 2

2. 2: 1

3. 1: 1

4. 4: 3

Consider an atom with atomic number Z as consisting of a positive point charge at the centre and surrounded by a distribution of negative charges uniformly distributed within a sphere of radius R. The electric field at a point inside the atom at a distance r from the centre is:

1. $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_{0}0}\left[\frac{1}{{\mathrm{r}}^2}-\frac{\mathrm{r}}{{\mathrm{R}}^3}\right]$

2. $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0}\left[\frac{1}{{\mathrm{r}}^2}+\frac{1}{{\mathrm{R}}^3}\right]$

3. $\frac{2\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0{\mathrm{r}}^2}$

4. Zero

An electron is rotating around an infinite positive linear charge in a circle of radius 0.1 m. If the linear charge density is 1 $\mathrm{\mu C}/\mathrm{m}$, then the velocity of the electron in m/s will be:

1. $0.582\times {10}^7$

2. $5.62\times {10}^7$

3. $562\times {10}^7$

4. $0.0562\times {10}^7$

For two infinitely long charged parallel sheets, the electric field at P will be:

1. $\frac{\mathrm{\sigma }}{2\mathrm{x}}-\frac{\mathrm{\sigma }}{2(\mathrm{r}-\mathrm{x})}$

2. $\frac{\mathrm{\sigma }}{2{\mathrm{\epsilon }}_0\mathrm{x}}+\frac{\mathrm{\sigma }}{2\mathrm{\pi }(\mathrm{r}-\mathrm{x}){\mathrm{\epsilon }}_0}$

3. $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0}$

4. Zero