Three charges q1, q2 and q3 are placed at the corner of an equilateral triangle
ID: 2132613 • Letter: T
Question
Three charges q1, q2 and q3 are placed at the
corner of an equilateral triangle where each
side has a length a. The point P is at the
middle of the base line.
q1 =?3 q, q2 = 2 q, q3 = q. Find the work required to bring
another charge q4 from ? to the point P, where q4 = q.
Three charges q1, q2 and q3 are placed at the corner of an equilateral triangle where each side has a length a. The point P is at the middle of the base line. q1 =?3 q, q2 = 2 q, q3 = q. Find the work required to bring another charge q4 from ? to the point P, where q4 = q.Explanation / Answer
work done = q4 * Potential at P = q4 * (potential at P due to q1 + potential at P due to q2 + potential at P due to q3)
= q4 * [k * q1 / (a * cos 30) + k * q2 / (a/2) + k * q3 / (a/2)]
= q4 * [2 * k * q1 * sqrt(3) / (a * sqrt(3)) + 2 * k * q2 / a + 2 * k * q3 / a]
= q4 * [2 * k * sqrt(3) * q / a + 2 * k * 2 * q / a + 2 * k * q / a]
= q * [2 * k * sqrt(3) * q] / a + 5kq/a]
= q * [2 * 1.732 * kq / a + 5kq/a]
= q(3.464 kq/a + 5 kq/a)
= 8.464 k q^2 / a, where k = 9 * 10^9
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