Two point charges (q 1 = -2.8C and q 2 = 6.7 C) are fixed along the x-axis, sepa

Question

Two point charges (q1 = -2.8C and q2 = 6.7 C) are fixed along the x-axis, separated by a distance d = 9 cm. Point P is located at (x,y) = (d,d).

1) What is Ex(P), the value of the x-component of the electric field produced by q1 and q2 at point P?

2) What is Ey(P), the value of the y-component of the electric field produced by q1 and q2 at point P?

3) A third point charge q3 = 2.5 C is now positioned along the y-axis at a distance d = 9 cm from q1 as shown. What is Ex(P), the x-component of the field produced by all 3 charges at point P?

Explanation / Answer

1) Ex(P) = E1x(p) + E2x(p)

Ex(p) = [-k*q1*cos(theta)/(2*d^2)] + 0

cos(theta) = 0.09/(sqrt(2)*0.09) = 1/sqrt(2) = 0.707

Ex(p) = [-9*10^9*2.8*10^-6*0.707/(2*0.09^2)]

Ex(p) = -1.1*10^6 N/C

2) Ey(p) = E1y(p) + E2y(p)

Ey(p) = [-k*q1*sin(theta)/(2*d^2)] + [k*q2/d^2]

sin(theta) = 0.09/(sqrt(2)*0.09) = 1/sqrt(2) = 0.707

Ey(p) = [-9*10^9*2.8*10^-6*0.707/(2*0.09^2)] + (9*10^9*6.7*10^-6/0.09^2)

Ey(p) = -1.1*10^6 N/C

Ey(p) = 6.34*10^6 N/C

3) Ex(p) = -1.1*10^6 + (k*q3/d^2) = -1.1*10^6 + (9*10^9*2.5*10^-6/0.09^2)

Ex(p) = 1.67*10^6 N/C

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