H1.1/Four charges q1,q2,q3,q4 form four corners of a square with side r [mm]. a.

Question

H1.1/Four charges q1,q2,q3,q4 form four corners of a square with side r [mm].
a.what is the magnitude of the net electrostatic force at each corner ?
b.what is the magnitude and direction of the electric field at the center of the square ?

q1=6e , q2=8e , q3= -8e , q4= -6e , r= 0.2

Fig H1.1

H1.1/Four charges q1,q2,q3,q4 form four corners of a square with side r [mm]. a.what is the magnitude of the net electrostatic force at each corner ? b.what is the magnitude and direction of the electric field at the center of the square ? q1=6e , q2=8e , q3= -8e , q4= -6e , r= 0.2 Fig H1.1

Explanation / Answer

a.net electrocstatic force at each corner is F_net = F1 + F2 + F3 + F4 where F1 = k_e * (q1q2/r^2),k_e = (1/4pieo) = 9 * 10^9 Nm^2/C^2,1e = 1.6 * 10^-19 C and r = 0.2 m Similarly,F2 = k_e * (q2q3/r^2), F3 = k_e * (q3q4/r^2) and F4 = k_e * (q4q1/r^2) b.magnitude of electric field due to q1 is E1 = k_e * (q1/r1^2) r1 = (2)^1/2r/2 = (r/(2)^1/2) due to q2 is E2 = k_e * (q2/r2^2) r2 = (2)^1/2r/2 = (r/(2)^1/2) due to q3 is E3 = k_e * (q3/r3^2) r3 = (2)^1/2r/2 = (r/(2)^1/2) due to q4 is E4 = k_e * (q4/r4^2) r4 = (2)^1/2r/2 = (r/(2)^1/2) net electric field is E = (Ex^2 + Ey^2)^1/2 Ex = E1xcosA + E2xcosB + E3xcosC + E4xcosD and Ey = E1ysinA + E2ysinB + E3ysinC + E4ysinD angles are A = B = C = D = 45o direction of net electric field is X = tan^-1(Ey/Ex)

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