When charges q_a,q_b,and q_c are placed respectively at the corners a,b,and c of a right triangle,the potential at the midpoint of the hypotenuse is 20 V.When the charge q_a is removed,the potential at the midpoint becomes 15 V.When,instead,the charge q_b is removed (q_a and q_c both in place),the potential at the midpoint becomes 13 V.What is the potential at the midpoint if only the charge q_c is removed from the array of charges? A) 12 V B) 8 V C) 7 V D) 5 V

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Quizplus · Accepted Answer

The potential at the midpoint of the hypotenuse is given by:$$V = \frac{1}{4\pi\epsilon_0} \left(\frac{q_a}{r_a} + \frac{q_b}{r_b} + \frac{q_c}{r_c}\right)$$where r_a, r_b, and r_c are the distances from the charges to the midpoint.When q_a is removed, the potential becomes:$$V = \frac{1}{4\pi\epsilon_0} \left(\frac{q_b}{r_b} + \frac{q_c}{r_c}\right)$$When q_b is removed, the potential becomes:$$V = \frac{1}{4\pi\epsilon_0} \left(\frac{q_a}{r_a} + \frac{q_c}{r_c}\right)$$When q_c is removed, the potential becomes:$$V = \frac{1}{4\pi\epsilon_0} \left(\frac{q_a}{r_a} + \frac{q_b}{r_b}\right)$$We can see that the potential when q_c is removed is the same as the potential when q_a is removed. Therefore, the potential at the midpoint when only q_c is removed is 15 V.

When Charges Qa,qb,and Qc Are Placed Respectively at the Corners

When Charges Q_a,q_b,and Q_c Are Placed Respectively at the Corners