Question

Determine the total electric potential energy for the charge distribution with three chargers in a straight line

Answer 1

The total electric potential energy is $\frac{kq_{1} q_{3} }{r_{13} } + \frac{kq_{2} q_{3} }{r_{23} } + \frac{kq_{1} q_{2} }{r_{12} }$.

Electric Potential Energy of a System of Charges :

The system's electric potential energy is equal to the amount of work necessary to create a system of charges by guiding them toward their designated locations from infinity against the electrostatic force without accelerating them. The symbol for it is U.U=W=qV. Electrostatic fields are conservative, therefore the work is independent of the path.

Assume three charges q₁ , q₂ and q₃ bring from infinity to point P.

To bring  q₁ no work is done,

$V_{p} = \frac{kq_{1} }{r_{1} }$

where, V = electric potential energy.

            q = point charge.

            r = distance between any point around the charge to the point charge.

           k = Coulomb constant; k = 9.0 × 109 N.

Now bring q₂,

$V_{2} = \frac{kq_{2} }{r_{2} }$

Work done by q₁ ;

$W_{1} = V_{p} q_{2} = \frac{kq_{1}q_{2} }{r_{12} }$

Now bring  q₃,

$V_{3} = \frac{kq_{3} }{r_{3} }$

Work done on q₃ by q₁ and q₂

$W= q_{3} [ V_{1} + V_{2} ]$

    $=\frac{kq_{1} q_{3} }{r_{13} }$$+ \frac{kq_{2} q_{3} }{r_{23} } + \frac{kq_{1}q_{3} }{r_{12} }$

This work done is stored in the form of potential energy.

∴U=W= potential energy of three systems.

Learn more about electric potential energy here:

brainly.com/question/15801030

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