A point charge Q = 5 10⁻⁸ C is fixed at the origin. The work done by an external agent in moving a point charge q = 4 C from point A(0, 6, 8) m to point B(a, 4, 0) m is 1.8 10⁻⁴ J . The positive value of the coordinate a is ( 1 4 _ o = 9 10⁹ in SI units )

Step-by-step solution

Distance of point A from the origin: r_A = 0^2 + 6^2 + 8^2 = 10 m Distance of point B from the origin: r_B = a^2 + 4^2 + 0^2 = a^2 + 16 m The work done by an external agent in moving the charge q from A to B is given by: W = q(V_B - V_A) = q Q 4 ₀ ( 1 r_B - 1 r_A ) Substituting the given values: 1.8 10⁻⁴ = 4 10⁻⁶ 9 10^9 5 10⁻⁸ ( 1 a^2 + 16 - 1 10 ) 1.8 10⁻⁴ = 1.8 10⁻³ ( 1 a^2 + 16 - 0.1 ) 1.8 10⁻⁴ 1.8 10⁻³ = 1 a^2 + 16 - 0.1 0.1 = 1 a^2 + 16 - 0.1 1 a^2 + 16 = 0.2 a^2 + 16 = 5 Squaring both sides: a^2 + 16 = 25 a^2