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 = 4.36 cm. Assume that the +x-axis is to the right and the +y-axis is up along the page.)

(a) What is the total electric field at P, the center of the arc?

(b) Find the electric force that would be exerted on a

?4.89 nC

point charge placed at P.

magnitude     N/C direction     ---Select--- to the left ,to the right, upwards, downwards? Three point charges are located on a circular arc as shown in the figure below. (Let r = 4.36 cm. Assume that the +x-axis is to the right and the +y-axis is up along the page.) (a) What is the total electric field at P, the center of the arc? magnitude N/C direction ---Select--- to the left ,to the right, upwards, downwards? (b) Find the electric force that would be exerted on a ?4.89 nC point charge placed at P. magnitude N direction ---Select--- to the left ,to the right, upwards, downwards,?

Explanation / Answer

First we name the charges

q1 (the one on top) = +3.00 nC

q2 (the one in the middle) = -2.00 nC

q3 (the one at the bottom) = +3.00 nC

Thus, using the equation

E = kq/r^2,

where k = 8.99E9 Nm^2/C^2, q = the source charge, r = the distance of that reference point from the charge.

Thus, the magnitude of the electric field for each is, as r = 4.36 cm = 0.0436 m,

E1 = 1.419E4 N/C [towards quadrant 4]

E2 = -9.458E3 N/C [towards the -x axis]

E3 = 1.419E4 N/C [towards quadrant 1]

Now, we get the x and y components of these,

E1x = 12288 N/C

E1y = -7095 N/C

E2x = -9.458E3 N/C

E2y = 0 N/C

E3x = +12288 N/C

E3y = +7095 N/C

Thus, adding x and y components

Enetx = (12288 - 9458 + 12288) N/C = 15118 N/C

Enety = (-7095 + 0 + 7095) N/C = 0 N/C

Thus, as you see, the net electic field is purely along x.

Thus, the answer to part a) is

Part a: 1.51E4 N/C, to the right

******************************************************************

For part b, note that

F = Eq

Thus, as q = 4.89 nC = 4.89E-9 C

F = 15118 N/C * 4.89E-9 C

F = 7.39E-5 N [answer for part b]

DONE! It was nice working with you!

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