Physics question

Question

In the diagram, q₁ = -2.00 x 10-5 C, 92 +3.80 x 10-6 C, and q3 = +5.30 x 10-5 C. What is the electric potential energy U, for charge q2? Include the correct sign (+ or -).

Q1-Q2-Q3 (left to right) Q1 to Q2 has distance of 1.15 m. Q2 to Q3 has a distance of 2.88 m.

Unit=J

Answer 1

Solution:

The electric potential energy U_e is a scaler quantity that does not have any direction. In the case of three charges the total electric potentail energy is U_Te = ∑ k Qi Qj / r , so in the problem with three charges

U_Te = k ( q1q2/ r 12 + q1q3/ r13 + q2q3 / r23)

q1 = -2.00 x 10^-5 C, q2 = +3.8 x 10^-6 C, q3 = +5.3 x 10^-5 C, k = 9 x 10⁹ N.m²/ C²

r12 = 1.15 m, r13 = 1.15m + 2.88m = 4.03 m, and r23 = 2.88 m

U_Te = 9 x10⁹ N.m²/ C² { [-2.00 x10^-5 C )( 3.8 x10^-6 C/ 1.15 m] + [ (-2.00 x 10^-5 C)( 5.3 x10^-5 C) / 4.03m] +[(3.8 x 10^-6 C)( 5.3 x 10^-5 C / 2.88 m] }

U_Te = 9 x10⁹ N.m²/ C² ( -6.609 x 10^-11 C² / m -2.630 x 10^-10 C² / m + 6.993 x 10^-11 C² / m )

U_Te = 9 x10⁹ N.m²/ C² ( -2.592 x 10^-10 C²/ m ) = -2.332 N .m = -2.332 J (Joules)

Note the answer to the electric potential energy can be -ve because it is a scalar quantity