Given the following charges in the X-Y plane (distances measured in meters) q_1

Question

Given the following charges in the X-Y plane (distances measured in meters) q_1 = 5 mu C q_2 = 10 mu C @ [-2, 3] Find at the field point P (x = -6, y = -4) the following: (a) The F-field at the field point due to the source charges q1 and q2. Express in format (b) The resultant E-field at the field point. Express in "i" "j" format (c) The total electric potential (with respect to infinity) at the field point (d) The magnitude and single of the force on a charge Q = 2 mu C placed at the field point (c) The electrostatic potential energy of a charge Q = 2 mu C placed at the field point if its mass is m = 25 ng nd it is released from rest.

Explanation / Answer

q1 = -5 uC at (3 , -2)
q2 = 10 uC at (-2 , 3)
P(-6,-4)

(a)
r1 = sqrt( (3+6)^2 + (-2+4)^2) = 9.22
E1 = k*q1/r1^2 * 9/9.22 i^ + k*q1/r1^2 * 2/9.22 j^
E1 = (8.9*10^3*5)/9.22^2 * 9/9.22 i^ + (8.9*10^3*5)/9.22^2 *  2/9.22 j^
E1 = 511 i^ + 113.5 j^ N/C

r2 = sqrt( (-2+6)^2 + (3+4)^2) = 8.06
E2 = - k*q1/r1^2 * 4/8.06 i^ - k*q1/r1^2 * 7/8.06 j^
E2 = - (8.9*10^3*10)/8.06^2 * 4/8.06 i^ - (8.9*10^3*10)/8.06^2 * 7/8.06 j^
E2 = - 680 i^ - 1190 j^ N/C

(b)

Er = E1 + E2
Er = 511 - 680 i^ + 113.5 - 1190 j^
Er = - 169 i^ - 1076.5 j^

(c)
V = k*q1/r1 + k*q2/r2
V = - (8.9*10^3*5)/9.22 + (8.9*10^3*10)/8.06
V =  6215.7 V

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