Question

(4) Consider four charged particles fixed at the corners of a square with a side length of 5 cm, see figure. The particles have charges q1--10 nC, q2 +10 nC, q3--20 nC, and q4 +10 nC. In unit vector notation, what net electric field do the particles produce at the square's center? yA q1 2 q4 q3

Answer 1

The diagonal length = 2x (2x)^2 = 5^2 + 5^2 = 2 times 9^2 2x = squareroot 2(5) x = 5 squareroot 2/2 = 5/squareroot 2 cm At the centre of the square the electric field due to q_2 and q_4 are equal in magnitude but opposite in directions Hence they cancel each other Net field at centre is only due to 'q_1' and 'q_2' The Electric field vector is component form, E = (E_3/squareroot 2 - E_1/squareroot 2)i + (E_1/squareroot 2 - E_3/squareroot 2)j E = E_3 - E_1/squareroot 2[i - j] E_3 = 9 times 10^9 times 20 times 10^- 9/25/2 times 10^- 4 = 144 times 10^3 NC^- 1 therefore E = (144 - 72)/squareroot 2 10^3 (i - j) E = 72 times 10^3/squareroot 2 (i - j) E_1 = 1/4 pi epsilon_0 a_1/x^2 = 9 times 10^9 times 10 times 10^- 9/(5/squareroot 2)^2 times 10^- 4 = 90 times 2/25 times 10^4 = 72 times 10^3 NC^- 1