A charge Q is located at a grid intersection in the x-y plane (see plot below),

Question

A charge Q is located at a grid intersection in the x-y plane (see plot below), with Q = 2.50 mu C The electric potential in the x-y plane due to a charge distribution near the origin is given V(x, y) = beta x/(x^2 + y^2)^3/2, with beta = 4.089 times 10^5 Nm^3/C, x and y in m. II. The electric potential V(x, y) is calculated at the locations N and U using the equation above. Its values are V_N = 8.452 times 10^3 Volts and V_U = 7.803 times 10^3 Volts. Calculate the y-component of the force on Q.

Explanation / Answer

relation between electric field and potential difference is

E = - dV/ dr

= - d/dr ( { * x / (x2 +   y2)3/2

= * [ i^ (y2 - 2 * x2)   +   j^ (x2 - 2 * y2)] / (x2 + y2)5/2

Ey   =      * {(x2 - 2 * y2) / (x2 + y2)5/2}

= 4.089 * 10^5 (   ( 6)^2 y - 2 (3)^2/ ( 6^2 + 3^2 ) ^5/2

=541.82 N/C

Fy = q Ey

= 2.5 * 10^-6 ( 541.82)

=1.35 * 10^-3 N

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