Answer to Question #171641 in Electric Circuits for Pranali Patil

Question #171641

You have two charges, a 1.7μC charge placed at the origin and a -3.6μC charge placed 2.0m to the right.  Determine where, on the line between the two charges, the electric potential difference will be zero.


1
Expert's answer
2021-03-16T11:20:28-0400

Let the distance from the 1.7μC charge to the point where the electric potential difference is zero be xx. Then, the distance from the -3.6μC charge to that point be 2x2-x. Then, we can write:


Vtotal=V1+V2=0,V_{total}=V_1+V_2=0,kq1r1+kq2r2=0,\dfrac{kq_1}{r_1}+\dfrac{kq_2}{r_2}=0,q1x+q22x=0,\dfrac{q_1}{x}+\dfrac{q_2}{2-x}=0,q1(2x)=q2x,q_1(2-x)=-q_2x,x=2q1q1q2=2 m1.7 μC1.7 μC(3.6 μC)=0.64 m.x=\dfrac{2q_1}{q_1-q_2}=\dfrac{2\ m\cdot1.7\ \mu C}{1.7\ \mu C-(-3.6\ \mu C)}=0.64\ m.

The electric potential difference will be zero at a distance of 0.64 meters from the 1.7μC charge and 1.36 meters from the -3.6μC charge.


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