Superposition of Electric Fields

Q. For the two fixed infinite line charges, the net electric field is zero at a point $\text{P}$ between them. The distance of the point $\text{P}$ from the left infinite line charge is

1. $1.25\text{m}$
2. $3.25\text{m}$
3. $2.25\text{m}$
4. $0.25\text{m}$

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. Two point charges $q_1=+9\mu C$ and $q_2=-1\mu C$ are held $10\text{cm}$ apart. Where should at third charge $+Q$ be placed from $q_2$ on the line joining them so that charge $Q$ does not experience any net force ?

Q. Two point charges $q_1=+9\mu C$ and $q_2=-1\mu C$ are held $10\text{cm}$ apart. Where should at third charge $+Q$ be placed from $q_2$ on the line joining them so that charge $Q$ does not experience any net force ?

1. $7\text{cm}$
2. $4\text{cm}$
3. $5\text{cm}$
4. $6\text{cm}$

Q. 5 equal charges $‘q^{\prime }$ each are placed at the corners of a regular hexagon $\text{ABCDEF}$ of side $‘a^{\prime }$ as shown. Find the net electric field at the centre $\text{O}$ of the hexagon?

1. $\frac{5kq}{a^2}$ towards $\text{F}$
2. $\frac{kq}{a^2}$ 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.

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. Zero

2. Along the diagonal AC

3. Along the diagonal BD

4. Perpendicular to side AB

Q. A thin uniformly charged ring of radius $1\text{m}$, charge $+10\text{C}$ and a semi-infinite charged wire of $\lambda =+10\text{nC/m}$, oriented along the axis of ring with one of its ends coinciding with the centre of the ring, form a system. Find the force of interaction between the ring and wire.

1. $600\text{N}$
2. $800\text{N}$
3. $900\text{N}$
4. $700\text{N}$

Q.

Two equal forces $\overrightarrow{F}$ are acting such that the magnitude of their resultant is equal to F. They must be inclined at an angle of __ degrees

Q. 5 equal charges $‘q^{\prime }$ each are placed at the corners of a regular hexagon $\text{ABCDEF}$ of side $‘a^{\prime }$ as shown. Find the net electric field at the centre $\text{O}$ of the hexagon?

1. $\frac{5kq}{a^2}$ towards $\text{F}$
2. $\frac{kq}{a^2}$ 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 electric potential $\left(V\right)$ in $\text{volts}$ varies with $x$ $\left(\text{in meters}\right)$ according to the relation $V=5+4x^2$. The force experienced by a negative charge of $2\mu C$ located at $x=0.5\text{m}$ is

1. $4\times {10}^{-6}\text{N}$
2. $2\times {10}^{-6}\text{N}$
3. $6\times {10}^{-6}\text{N}$
4. $8\times {10}^{-6}\text{N}$

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