On the axis of a uniformly charged ring of radius R, as shown, the electric field is maximum at

1.  x = 0

2.  $x = \frac{R}{2}$

3.  $x = R\sqrt{2}$

4.  $x = \frac{R}{\sqrt{2}}$

At the three corners of an equilateral triangle, charges are placed as shown in the figure. The magnitude of the electric field at point O is

1.  $\frac{1}{4\pi {\epsilon }_0}\frac{2Q}{r^2}$

2.  $\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}$

3.  $\frac{1}{4\pi {\epsilon }_0}\frac{Q\sqrt{2}}{r^2}$

4.  $\frac{1}{4\pi {\epsilon }_0}\frac{Q\sqrt{3}}{r^2}$

Two symmetrical parallel metal each of one side plate area A having charges $Q_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>-Q_2$ are placed at small separation. What will be the electric field at a point in between the plates?

1.  $\frac{Q_1+Q_2}{2A{\epsilon }_0}$

2.  $\frac{Q_1+Q_2}{4A{\epsilon }_0}$

3.  $\frac{Q_1-Q_2}{2A{\epsilon }_0}$

4.  $\frac{Q_1-Q_2}{4A{\epsilon }_0}$

An electric dipole of the moment $\overrightarrow{P}$ is released in a uniform electric field $\overrightarrow{E}$ from the position of maximum torque. The angular speed of the dipole when $\overrightarrow{P}$ becomes parallel to $\overrightarrow{E}$ will be [l = moment of inertia of dipole]

1.  $\sqrt{\frac{2PE}{I}}$

2.  $\sqrt{\frac{PE}{I}}$

3.  $\sqrt{\frac{4PE}{I}}$

4.  $\sqrt{\frac{2I}{PE}}$

A charge Q is given to a conducting sphere of radius R. Now if a charge -Q is placed, as shown, at a distance r from the center, then the magnitude of the force of attraction between charges is

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

2.  <$\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{Q^2}{r^2}$

3.  >$\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{Q^2}{r^2}$

4.  $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{Q^2}{{\left(r-R\right)}^2}$

If the electric flux entering and leaving a closed surface are respectively of magnitude ${\varphi }_1<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{\varphi }_2$, then the electric charge inside the surface will be

1.  ${\epsilon }_0\left({\varphi }_2-{\varphi }_1\right)$

2.  $\left({\varphi }_1-{\varphi }_2\right){\mathrm{/2\epsilon }}_0$

3.  ${\epsilon }_0\left({\varphi }_2+{\varphi }_1\right)$

4.  $\frac{{\varphi }_2-{\varphi }_1}{{\epsilon }_0}$

Electric field at an axial point of short dipole is  $\overrightarrow{E_1}$. If the electric field at the equatorial point of same dipole is $\overrightarrow{E_2}$, then which of the following is correct?

1.  $\overrightarrow{E_1}$ . $\overrightarrow{E_2}$ < 0

2.  $\overrightarrow{E_1}$ . $\overrightarrow{E_2}$ > 0

3.  $\overrightarrow{E_1}$ . $\overrightarrow{E_2}$ = 0

4.  $\overrightarrow{E_1}$ . $\overrightarrow{E_2}$ = $\overrightarrow{0}$

A long thin rod is charged such that charge per unit length of the rod is $\lambda$. The rod is inserted into a hollow spherical surface of radius R. Maximum electric flux coming out the surface is

1.  $\frac{\lambda R}{{\epsilon }_0}$

2.  $\frac{2\lambda \pi R^2}{{\epsilon }_0}$

3.  $\frac{2\lambda R}{{\epsilon }_0}$

4.  $\frac{2\lambda R^2}{{\epsilon }_0}$

Two charges q and 4q are separated by a distance r. The neutral point(in between the line joining the charges) is at a distance:

1.  $\frac{r}{3}\mathrm{from}<mspace\; width="1em"></mspace>q$

2.  $\frac{2r}{3}\mathrm{from}<mspace\; width="1em"></mspace>q$

3.  $2r<mspace\; width="1em"></mspace>\mathrm{from}<mspace\; width="1em"></mspace>q$

4.  $r<mspace\; width="1em"></mspace>\mathrm{from}<mspace\; width="1em"></mspace>4q$

A positron and a proton are projected normally into a uniform electric field with equal kinetic energy. The trajectory followed by them are: