Superposition of Electric Fields

Q.

5 equal charges ‘q’ are placed at corners of a regular hexagon ABCDEF of side ‘a’ as shown. Find the net electric field at the centre O of the hexagon?

1. $\frac{kq}{a^2}$ towards $\text{F}$
2. $\frac{5kq}{a^2}$ towards $\text{F}$
3. $3\sqrt{2}\frac{kq}{a^2}$ towards $\text{F}$
4. $5\sqrt{2}\frac{kq}{a^2}$ towards $\text{C}$

Q. The three charges $\frac{q}{2},q$ and $\frac{q}{2}$ are placed at the corners $A,B$ and $C$ of a square of side $‘a^{\prime }$ as shown in figure. The magnitude of electric field $\left(E\right)$ at the corner $D$ of the square is

1. $\frac{q}{4\pi {\epsilon }_0{a}^2}(\frac{1}{\sqrt{2}}-\frac{1}{2})$
2. $\frac{q}{4\pi {\epsilon }_0{a}^2}(1+\frac{1}{\sqrt{2}})$
3. $\frac{q}{4\pi {\epsilon }_0{a}^2}(1-\frac{1}{\sqrt{2}})$
4. $\frac{q}{4\pi {\epsilon }_0{a}^2}(\frac{1}{\sqrt{2}}+\frac{1}{2})$

Q.

Four charges are arranged at the corners of a square ABCD , as shown in the adjoining figure. The force on the charge kept at the centre O is

1. Along the diagonal BD
2. Perpendicular to side AB
3. Zero
4. Along the diagonal AC

Q. Two charges $40nC$ & $10nC$ are placed $60cm$ apart. At what point do we get the value of net electric field equal to zero?

1. $20cm$ from $40nC$
2. $10cm$ from $10nC$
3. $20cm$ from $10nC$
4. $40cm$ from $10nC$

Q. Three charges 4q, Q and q are in a straight line in the position of 0, $\frac{l}{2}$ and l respectively. The resultant force on q will be zero, if Q =

1. -q
2. $-\frac{q}{2}$
3. 4q
4. -2q

Q. There are two equal but opposite charges in space. The field at the mid point of the two charges is times the field due to individual charges.

1. two
2. three
3. four
4. zero

Q. Consider a regular cube with positive point charge $+Q$ in all corners except for one which has a negative point charge $-Q$. Let the distance from any corner to the center of the cube be $r$. What is the magnitude of electric field at point $P$, the center of the cube?

1. $E=\frac{7kQ}{r^2}$
2. $E=\frac{1kQ}{r^2}$
3. $E=\frac{2kQ}{r^2}$
4. $E=\frac{6kQ}{r^2}$

Q. Consider a small positive charge $q$ and mass $m$ placed as shown, between two positive charges $Q$ (fixed) each. For a small push given to $q$ as shown, find the time period of simple harmonic oscillations.

1. $T=2\pi \sqrt{\frac{m{a}^2\pi {\in }_0}{Qq}}$
2. $T=2\pi \sqrt{\frac{m{a}^2\pi {\in }_0}{Qq}}$
3. $T=2\pi \sqrt{\frac{m{a}^3\pi {\in }_0}{3Qq}}$
4. $T=2\pi \sqrt{\frac{3m{a}^3\pi {\in }_0}{Qq}}$

Q.

Two particles A and B, each arrying a charge Q, are held fixed with a separation d between them. A particle C having mass m and charge q is kept at the middle point of the line AB. (a) if it is displaced through a distane x perpendicular to AB, what would be the electric forc experienced by it (b) Assuming x<<d, show that this force is proportional to x. (c) Under what conditions will the particle C execute simple harmonic motion if it is released after such a small displacement? Find the time perio of the oscillations if these conditions are satisfied.

Q.

The bob of a simple pendulum has a mass of 40 g and a positive charge of $4.0\times {10}^{-6}C.$ It makes 20 oscillations in 45 s. A vertical electric field pointing upward and of magnitude $2.5\times {10}^{4}N{C}^{-1}$ is switched on. How much time will it now take to complete 20 oscillations?