Question

Identical point charges of +2.1 ìC are fixed to diagonally opposite corners of a square. A third charge is then fixed at the center of the square, such that it causes the potentials at the empty corners to change signs without changing magnitudes. Find the sign and magnitude of the third charge.

Answer 1

q=2.1μC=2.1•10⁻⁶ C,
the side of square ia “a” .
The potential at the empty corner due to two charges
φ=φ₁+φ₂ = kq/a + kq/a= 2kq/a
The potential at the empty corner due to three charges
φ`=φ₁+φ₂ +φ₃= kq/a + kq/a + kq₀2/(a√2)= 2kq/a + kq₀2/(a√2).
By the data
φ`= - 2kq/a, =>
2kq/a + kq₀2/(a√2) = - 2kq/a
kq₀2/(a√2) = - 4kq/a
q₀=2√2q=2•1.41•2.1•10⁻⁶ =5.94•10⁻⁶ C