Superposition of Electric Fields

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

1. zero
2. along the diagonal AC
3. perpendicular to side AB
4. along the diagonal BD

Q.

A positively charged pendulum is oscillating in a uniform electric field pointing upwards. It's time period as compared to that when it oscillates without electric field is more How?

Q.

A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)

Q. A charge $Q$ is enclosed by a Gaussian spherical surface of radius $R$. If the radius is doubled, then the outward electric flux will

1. be reduced to half
2. remain the same
3. be doubled
4. become four times

Q. 13. A wire is bent in the form of a regular pentagon of edge length a. A total of charge q is distributed over it.Find the electric field at the centre of the pentagon

Q. ABCD is a square of side 5cm. Charges of +50 C, -50C, and +50C are placed at A, C and D respectively.Find the resul†an t elctric field at B

Q. two equal and like charges when placed 5 cm apart experience a repulsive force of 0.144 newtons. The magnitude of the charge in micro-coulomb will be

Q. Consider three charges q1, q2, q3 each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q(with the same sin as q) placed at the centroid of the triangle?

Q.

Two fixed point charges + 4ee and +e units are separated by a distance 'a'. Where should the third point charge be placed for it to be in equilibrium?

Q.

A particle of mass $$m$$, charge $$Q$$and kinetic energy$$T$$enters a transverse uniform magnetic field of induction $$\overrightarrow{B}$$. After $3$ seconds the kinetic energy of the particle will be:

1. $$3T$$

2. $2T$

3. $$T$$

4. $$4T$$

Q. Four charges Q, q, Q and q are kept at the four corners of a square. What is the relation between Q and q so that the net force on a charge q is 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.

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?

Q. 91.A positively charged pendulum is oscillating in a uniform electric field pointing upwards.Its time period as compared to that when it oscillates without electric field is more or less.

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 resultant of two equal forces is equal to either of these forces. The angle between them is

1. $\frac{\mathrm{\pi }}{4}$

2. $\frac{\mathrm{\pi }}{3}$

3. $\frac{\mathrm{\pi }}{2}$

4. $\frac{2\mathrm{\pi }}{3}$

Q. 131. A point charge is placed at distance a/2 perpendicular to the plane and above the centre of a square ofa side a .the electric flux through the square is

Q. 41. There are two charges +2uC and -3uC.the ratio of forces acting on them will be

Q. For the given graph between electric field $\left(E\right)$ at a point and distance $\left(x\right)$ of this point from the mid-line of an infinitely long uniformly charged non-conducting thick sheet, the volume charge density of the given sheet is:-
[$d$ is the thickness of the sheet]

1. $3\times {10}^{-12}{\text{C/m}}^3$
2. $9\times {10}^{-12}{\text{C/m}}^3$
3. $12\times {10}^{-12}{\text{C/m}}^3$
4. $15\times {10}^{-12}{\text{C/m}}^3$

Q.

A wire is bent in th eform of a regular hexagon and a total cahrge q is distributed uniformly on it. What is the electric field at the centre? you may answer this part without making any numerical calculations.

Q. 29. How to find net electric field of hexagon of side 1m with six point charges -q -q -q q q q

Q.

A small circular ring has a uniform charge distribution. On a far off axial point distance x from the centre of the ring the electric field is proportional to?

Q. Three charges +q, -q and +q are kept at the corners of an equilatral triangle of side d. Find the resul†an t electric force on charge +q placed at the centriod o of the triangle

Q.

A string, fixed at both ends, vibrates in a resonant mode with a separation of 2.0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. Find the length of the string.

Q. A, B, C, D corners of square of side 2a are occupied by q, -q, 2Q, Q charges resp. the fiepd at midpoint of Cd is zero. what id value of q/Q

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. Figure 1.33 shows tracks of three charged particles in a uniformelectrostatic field. Give the signs of the three charges. Which particlehas the highest charge to mass ratio?

Q.

A particle is acted upon by four forces simultaneously, $30N$ due east $20N$ due north $15N$ due west $40N$ due south find the resultant force of the particle?

Q. 28.Two charged capacitor have their outer plates fixed and inner plates connected by spring of force constant k . The charge on each capacitor is q . Find the extension in the spring at equilibrium?

Q. two charges 2q and -3q are kept on a straight line , the number of points on this line where the electric field intensity os zero is