Name: Equipotential Surfaces and Its Properties
Uploaded: 2019-07-19
Duration: 7 min 22 s
Description: The surface over which the electric potential is the same everywhere is called an equipotential surface. Let's more about it and its properties in this video.

Question

Three point charges $+ 1 μ C, - 1 μ C$ and $+ 2 μ C$ are initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side $10 cm$ . Take $(\frac{1}{4 π ε_{o}}) = 9 \times 10^{9} N m^{2} C^{- 2}$

Accepted Answer

A possible configuration of the three charges is shown below.

No external field is present and, the charges are initially infinite distance apart. Hence, the work done in bringing the first charge $(+ 1 μC)$ at A from infinity will be zero.

$W_{1} = 0$ .....(i)

The potential at point B due to the first charge $(+ 1 μC)$ , at a distance of $10 cm$ , from the charge A:

$V_{1} = 9 \times 10^{9} \times \frac{1 \times 10^{- 6}}{10 \times 10^{- 2}} = 9 \times 10^{4} J / C$

Work done in bringing $- 1 μC$ charge at point B:

$W_{2} = - 1 \times 10^{- 6} \times 9 \times 10^{4} = - 9 \times 10^{- 2} J$ .....(ii)

The potential at point C due to the charge present at A:

$V_{2} = 9 \times 10^{4} J / C$

The potential at point C due to the charge present at B:

$V_{3} = \frac{9 \times 10^{9} \times (- 1) \times 10^{- 6}}{10 \times 10^{- 2}} = - 9 \times 10^{4} J / C$

The work done on $+ 2 μ C$ will be due to two charges that are already present. The total work done on it:

$W_{3} =$ Work done due to charge present at A+ Work done due to the charge present at B

$W_{3} = 2 \times 9 \times 10^{4} + 2 \times (- 9 \times 10^{4}) = 0$

The total work done in assembling the three given charges, as shown in the above diagram:

$W_{1} + W_{2} + W_{3} = - 9 \times 10^{4} J$

The work-done in assembling the three charges will be $- 9 \times 10^{4} J$ .

Three point charges $+ 1 μ C, - 1 μ C$ and $+ 2 μ C$ are initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side $10 cm$ . Take $(\frac{1}{4 π ε_{o}}) = 9 \times 10^{9} N m^{2} C^{- 2}$

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Three point charges +1 μC, -1 μC and +2 μC are initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side 10 cm. Take 14πεo=9×109 N m2C-2

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Three point charges $+ 1 μ C, - 1 μ C$ and $+ 2 μ C$ are initially infinite distance apart. Calculate the work done in assembling these charges at the vertices of an equilateral triangle of side $10 cm$ . Take $(\frac{1}{4 π ε_{o}}) = 9 \times 10^{9} N m^{2} C^{- 2}$