Three point charges are located on a circular arc as shown in the figure below.

Question

Three point charges are located on a circular arc as shown in the figure below. (Let r = 3.60 cm. Let to the right be the +x direction and up along the screen be the +y direction.)

?4.51 nC

Three point charges are located on a circular arc as shown in the figure below. (Let r = 3.60 cm. Let to the right be the +x direction and up along the screen be the +y direction.) (b) Find the electric force that would be exerted on a ?4.51 nC point charge placed at P. (a) What is the total electric field at P, the center of the arc?

Explanation / Answer

Here ,

as point P , field due to 3 nC charge

E3 = k*q/r^2

E3 = 9*10^9*3 *10^-9 /.036^2

E3 = 2.08 *10^4 N/C

Now,

due to charge 2 nC

E2 = 9*10^9*2 *10^-9 /.036^2

E2 = 1.39 *10^4 N/C

Now , y - component of the field cancels due to symmetry

Now, the net field at P is

Ep = (1.39 *10^4 - 2 * 2.08 *10^4 * cos(30)) i

Ep = 2.22 *10^4 i N/c + 0 j

the total electric field at P, the center of the arc is 2.22 *10^4 i N/c + 0 j

B)

Force = q*E

FOrce = -4.51 *10^-9 *(2.22 *10^4 i N/c + 0 j )

Force = - 1.0 *10^-4 i + 0 j N

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