Suppose three point charges are arranged as shown in the figurebelow. A charge q

Question

Suppose three point charges are arranged as shown in the figurebelow. A charge q1 = +1.5 µC is located at the origin of anx-, y-coordinate system; a second chargeq2 = -0.55 µC islocated at (1.20 m, 0.50 m) and the third chargeq3 = +0.18 µC islocated at (1.20 m, 0). Find the magnitude of the force onq2 due to the other two charges,q1 and q3. [Hint: Afterfinding the force on q2 due toq1, separate that force into x- andy-components.] The answer is in mN

Suppose three point charges are arranged as shown in the figurebelow. A charge q1 = +1.5 µC is located at the origin of anx-, y-coordinate system; a second chargeq2 = -0.55 µC islocated at (1.20 m, 0.50 m) and the third chargeq3 = +0.18 µC islocated at (1.20 m, 0). Find the magnitude of the force onq2 due to the other two charges,q1 and q3. [Hint: Afterfinding the force on q2 due toq1, separate that force into x- andy-components.] The answer is in mN

Explanation / Answer

The force acting between charges q1 andq2 is F1 = k *(q1q2/r2) k = (1/4o) = 9 * 109Nm2/C2,q1 = +1.5 C = +1.5 *10-6 C,q2 = -0.55 C = -0.55 *10-6 C and r2 = [(1.20 - 0)2 + (0.50 -0)2] = 1.69 m2 The force acting between charges q3 andq2 is F2 = k *(q3q2/r12) q3 = +0.18 C = +01.8 *10-6 C and r12 = [(1.20 -1.20)2 + (0 - 0.50)2] = 0.25m2 The resultant force acting on the charge q2is Fr = (Fx2 +Fy2)1/2 where Fx = F1x + F2x =F1 * cos1 + F2 *cos2 and Fy = F1y + F2y =F1 * sin1 + F2 *sin2 The angles are tan1 = (0.50 - 0/1.20 - 0) =(0.50/1.20) or 1 = tan-1(0.50/1.20) =22.6o and tan2 = (0.50 - 0/1.20 - 1.20) =(0.50/0) or 2 = tan-1() =90o and tan2 = (0.50 - 0/1.20 - 1.20) =(0.50/0) or 2 = tan-1() =90o

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