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Three infinitely long straight line charges with linear charge densities lambda, lambda, and -2*lambda are placed in space. A point in space is described by its perpendicular distances r1, r2, and r3 from the three line charges respectively. What is the condition for a set of points to be equipotential?
- r1*r2 / r3² = constant
- r1*r2*r3² = constant
- r1*r2*r3^(1/2) = constant
- r1*r2*r3 = constant
Correct answer: r1*r2 / r3² = constant
Solution
Potential from line charge density lambda at distance r: V = -(lambda/(2*pi*epsilon0))*ln(r) + C. Total potential from all three charges: V_total = -(1/(2*pi*epsilon0))*[lambda*ln(r1) + lambda*ln(r2) - 2*lambda*ln(r3)] = -(lambda/(2*pi*epsilon0))*ln(r1*r2/r3²). For equipotential surface: r1*r2/r3² = constant.
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