A - 14 ? C charge is placed on the x-axis at the origin. Two + 14 ? C charges ar

Question

A -14 ?C charge is placed on the x-axis at the origin. Two +14 ?C charges are placed on the y-axis: one at y = +0.1 m and one at y = -0.1 m. Consider a point A which is on the x-axis at x =0.2 m. (for all answers below assume the unit vectors x^ and y^ point towards positive x and positive y.).

a.What is the x-component of the electric field at the point A? (N/C)

b.What is the y-component of the electric field the point A? (N/C)

c.If you put a charge q = -1

?C at the point A, what is the x-component of the force?  (N)

d. If you put a charge q = -1

?C at the point A, what is the y-component of the force? (N)

Thanks

Explanation / Answer

a) vertical components of Electric field due to +ve charges cancel out.

Enet = E1 + E2 + E3

Enet(1,2) = 2* 9*10^9*14*10^-6 / (0.1^2 + 0.2^2) = 5.04*10^6 (cos(theta) ) i

theta = arctan(1/2) = 26.57

Enet(1,2) = 5.04*10^6 * cos(26.57 deg) = 4.51*10^6 (i) N/C

E3 = 9*10^9*14*10^-6 / 0.2^2 = 3.15*10^6 (-i) N/C

Enet = 1.36 * 10^6 i N/C

a)

x-component = 1.36 * 10^6 N/C

b)

y-component = 0

c)

F = E*q = 1.36*10^6*10^-6 = 1.36 N

d)

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