Numerical's Solution (Electric Field & Electric Potential):

[2076 B]
Three equal charges $1.8 * 10^{-6}\;C$ each are located at the corners of an equilateral triangle ABC of side $10\;cm$. Calculate the electric potential due to these charges at the mid point of AB. [Click here for Solution]

[2075 S / 2068 S]

Calculate the value of two equal charges if they repel one another with a force of $0.1\;N$, when situated $50\;cm$ apart in vacuum. What would be the distance if they are placed in an insulating medium of dielectric constant $10$ ? [Click here for Solution]

[2075 'A']
Two large parallel metal plates carry opposite charges. They are separated by $10 \;cm$ and potential difference of $500 \;V$ is applied of them. 

a) What is the magnitude of electric field strength between them?

b) Compute the work done by this field on a charge of $2 * 10^{-9}\;C$ as it moves from higher to the lower potential.  [Click here for Solution]

[Ans: $500 V/m$; $10^{-6}J$]

[2075 'B']

Two large parallel metal plates carry opposite charges. They are separated by $0.2 \; m$ and potential difference of $500\;V$ is applied of them.What is the magnitude of electric field if it is uniform, in the region between them?  [Click here for Solution]

[Ans: $2500 V/m$]

[2072 'C'; Supp. 2070 'A']

What distance must an electron move in a uniform potential gradient $200\;V/cm$ in order to gain kinetic energy $3.2 * 10 ^{-18}J$?  [Click here for Solution]

[Ans: $0.001\;m$]

[2072'D'].
An electron of mass $9.1 * 10^{-31}\;kg$ and charge $1.6 * 10^{-19}\;C$ is situated in a uniform electric field of intensity $1.2 * 10^{4}\;Vm^{-1}$. Find the time it takes to travel $1\; cm$ from rest.  [Click here for Solution]

[Ans: $t = 3.07 * 10^{-9}$Sec]

[2072'E'].

A solid sphere of radius $1\;cm$ is carrying a charge of $2\;C$. Find the electric field intensity at the center, on its surface and at a point $2\;cm$ from the center of the charged sphere. [Click here for Solution]

[Supp. 2071].

An alpha particle is a nucleus of doubly ionized helium. It has mass of $6.68 * 10^{-27}$kg and charge of $3.2 * 10^{-19}C$. Compare the force of electrostatic repulsion between the two alpha particles with the force of gravitational attraction between them. [Click here for Solution]

[Ans: $3.1 * 10^{35}$]

[2070 Supp. 'B']
An electric charge $1.6 * 10^{-19} \;C$ is situated in a uniform electric field of intensity 120,000 V/m. Find the force on it and its acceleration. [Click here for Solution]

[Supp. 2069].

Two charge of $2\mu C$ and $4\mu C$ are placed $2\;m$ apart. Find a point on the line joining the charges where the electric field intensity will be zero. [Click here for Solution]

[2069 'A'].

Two charges $+1 * 10^{-6} C$ and $-4 * 10^{-6} C$are separated by a distance of $2m$. Determine the position of the null point. [Click here for Solution]

[Ans: $2\;m$]

[2068 OLD]
Two horizontal parallel plates, 200 mm apart, having a potential difference of 1000 V between them the upper plate being at a positive potential. A negatively - charged oil drop, mass $4.8 * 10^{-15}\;kg$ is situated between the plates. Calculate the number of electrons on the drop if it is stationary in the air, neglecting the density of air. [Click here for solution]

[2067].
A hollow spherical conductor of radius 12 cm is charged to $6*10^{-6}C$. Find the electric field strength at the surface of sphere, inside the sphere at $8\;cm$ and at distance $15 \; cm$ from the sphere. [Click here for Solution]

[Ans: $3.75 * 10^{6}N/C; 0\;(Zero); 7.41 * 10^{5} N/C$]

[2066]
Two horizontal parallel plates each of area $500\;cm^2$ are mounted 2 mm apart in vacuum. The lower plate is earthed and the upper one is given a positive charge of $0.05\;\mu C$. Find the electric field intensity and the potential difference between the plates. [Click here for solution]

[2054]
Three equal charges $1.8 * 10^{-6}\;C$ each are located at the corners of an equilateral triangle ABC, whose sides are 6 cm. Calculate the electric potential at a point midway between AB. [Click here for solution]

[2052]
A charged oil drop remains stationary when situated between two parallel horizontal plates 30 mm apart and a p.d. of 1000 V is applied to the plates. Find the charge on the oil drop if it has mass of $6 * 10^{-15}\; kg$. Assume $g = {9.8\;m/s^2}$. [Click here for Solution]

[2051]
Three equal charges of $4.0 * 10^{-7}\;C$ are located at the corners of a right triangle whose sides are $6 \;cm$, $8 \; cm$ and $10 \; cm$ respectively. Find the force exerted on the charge located at $90^{\circ}$ angle. [Click here for Solution]

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