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. (Taker=4.40cm. Let to the right be the +xdirection and up along the screen be the +ydirection.)

Three point charges are located on a circular arc as shown in the figure below. (Taker=4.40cm. Let to the right be the +xdirection and up along the screen be the +ydirection.) 1 (a) What is the total electric field atP, the center of the arc? E=i hat + j hat (b) Find the electric force that would be exerted on a-4.96 nC point charge placed atP. F =i hat + j hat

Explanation / Answer

The horizontal components of electric field due to charges q_1 ,q_2 and _q_3
E_x = E_1x + E_2x +E_3x

E_x = (kq_1 / r^2 )cos30^0 + (kq_2 /r^2) cos180^0 + (kq_3 / r^2 )cos30^0

Here r = radius of the circular arc = 4.4*10^-2 m
charges q_1 = q_3 = 3.0*10^-9 N and q_2 = -2.0*10^-9 C
k = 9*10^9 N.m^2 /C^2
plug all the values we get

E_x = 1.2*10^4 N/C - 0.9297 *10^4 N/C + 1.2077*10^4 N/C
E_x = 1.478*10^4 N/C

The verticle components of electric field at point p
E_2y = 0
As shown in the diagram E_1y and E_3y are cancells each other
E_y = 0
hence net electric field at the centre P E = sqrt ( (E_x)^2 + (E_y)^2) = 1.795*10^4 N/C
direction towards right
(b)
The force on the charge charge -4.95 nC
F =E *q = ( 1.478*10^4 N/C )(4.95*10^-9 C) = 7.3161*10^-5 N

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