A plastic rod has been bent into a circle of radius R = 6.50 cm. It has a charge

Question

A plastic rod has been bent into a circle of radius R = 6.50 cm. It has a charge Q1 = +8.16 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1 uniformly distributed along the rest of the circumference (see the figure). With V = 0 at infinity, what is the electric potential in volts (a) at the center C of the circle and (b) at point P, which is on the central axis of the circle at distance D = 3.59 cm from the center?

A plastic rod has been bent into a circle of radius R = 6.50 cm. It has a charge Q1 = +8.16 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1 uniformly distributed along the rest of the circumference (see the figure). With V = 0 at infinity, what is the electric potential in volts (a) at the center C of the circle and (b) at point P, which is on the central axis of the circle at distance D = 3.59 cm from the center?

Explanation / Answer

The electric potenital at the center is given as

V = (k q1 /R ) + (k q2 / R)

= (k q1 /R ) + (k q2 / R)

= - 5 k q1 /R

= - 5 (8.99x10^9 )( 8.16x10^-12) / (0.065m)

= - 5.649 V

The potential at a distace D from the center is

V = - 5 k q1 / ?[ R^2 / d^2 ]

= - 5 (8.99x10^9)(8.16 x10^-12) / ?[ 0.0359)^2 + (0.065)^2 ]

= - 4.945 V

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