Three charges, q 1 = +3.32nC, q 2 = -1.41nC, and q 3 = +8.61nC, are at the corne

Question

Three charges, q1 = +3.32nC, q2 = -1.41nC, and q3 = +8.61nC, are at the corners of an equilateral triangle, each of whose sides are of length, L, as shown in the figure below.

The angle is 60.0° and L = 0.572 m. We are interested in the unmarked point midway between the charges q1 and q2 on the x axis.

1) For starters, calculate the magnitude and direction of the electric field due only to charge q1 at this point. 3.65E2 N/C to the right. This answer is correct.

2) Calculate the magnitude and direction of the electric field due only to charge q2 at this point. 1.55E2 N/C to the right. This is correct.

3) Calculate the magnitude and direction of the electric field due only to charge q3 at this point. I know that the charge moves down but I cant figure out how to find the value.

4) Now calculate the magnitude of the electric field from all three charges at a point midway between the two charges on the x axis.

5) Calculate the angle of the electric field relative to the positive (to the right) x-axis, with positive values up (counterclock-wise) and negative down (clockwise). (enter the answer with units of deg)

6) If a tiny particle with a charge q= 1.24nC were placed at this point midway between q1 and q2, what is the magnitude of the force it would feel?

Help would be greatly apprciated!

Three charges, q1 = +3.32nC, q2 = -1.41nC, and q3 = +8.61nC, are at the corners of an equilateral triangle, each of whose sides are of length, L, as shown in the figure below. The angle I plusminus is 60.0Adegree and L = 0.572 m. We are interested in the unmarked point midway between the charges q1 and q2 on the x axis. For starters, calculate the magnitude and direction of the electric field due only to charge q1 at this point. 3.65E2 N/C to the right. This answer is correct. Calculate the magnitude and direction of the electric field due only to charge q2 at this point. 1.55E2 N/C to the right. This is correct. Calculate the magnitude and direction of the electric field due only to charge q3 at this point. I know that the charge moves down but I cant figure out how to find the value. Now calculate the magnitude of the electric field from all three charges at a point midway between the two charges on the x axis. Calculate the angle of the electric field relative to the positive (to the right) x-axis, with positive values up (counterclock-wise) and negative down (clockwise). (enter the answer with units of deg) If a tiny particle with a charge q= 1.24nC were placed at this point midway between q1 and q2, what is the magnitude of the force it would feel?

Explanation / Answer

1) distance from q1 to the point, r1 = 0.572/2 = 0.286 m

E1 = k*q1/r1^2 = 9*10^9*3.32*10^-9/0.286^2 = 3.65*10^2 N/C (towards right)

2)distance from q1 to the point, r2 = 0.572/2 = 0.286 m

E2 = k*q2/r2^2 = 9*10^9*1.41*10^-9/0.286^2 = 1.55*10^2 N/C (towards right)

3) distance from q3 to the point, r3 = sqrt(L^2-r1^2) = sqrt(0.572^2-0.286^2) = 0.495 m

E1 = k*q3/r3^2 = 9*10^*8.61*10^-9/0.495^2 = 3.163*10^2 N/C (towards down)

4) Ex = E1 + E2 = 5.2*10^2 N/C
Ey = E3 = -3.163*10^2 N/C

Enet = sqrt(Ex^2 + Ey^2) = 6.09*10^2 N/C

5) theta = tan^-1(Ey/Ex) = tan^-1(-3.163/5.2) = -31.31 degrees (clockwsie)


6) F = q*Enet = 1.24*10^-9*6.09*10^2 = 7.55*10^-7 N

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