Point charge q 1 = -5.00 nC is at the origin and point charge q 2 = +3.00nC is o

Question

Point charge q1 = -5.00 nC is at the origin and point charge q2 = +3.00nC is on the x -axis at x= 3.00cm. Point P is on the y-axis at y = 4.00cm.

Calculate the electric fields E 1 and E 2 at point P due to the charges q1 and q2. Express your results in terms of unit vectors (see example 21.6 in the textbook).

Express your answer in terms of the unit vectors i^, j^. Enter your answers separated by a comma.

E1,E2=

Use the results of part (a) to obtain the resultant field at P, expressed in unit vector form.

Express your answer in terms of the unit vectors i^, j^.

Explanation / Answer

q1 = -5.00 nC @ x =0
q2 = 3.00 nC @ x =3 cm
P is on the y-axis at y = 4.00cm

E1 = k *q1 / r^2
E1 = 8.9 * 10^9 * 5 * 10^-9 / (0.04)^2
E1 = 2.78 * 10^4 N/C

E1 = - 2.78 * 10^4 j N/C

E2 = k *q2 / r2^2
E2 = 8.9 * 10^9 * 3 * 10^-9 / ((0.04)^2 + (0.03)^2)
E2 = 1.07 * 10^4 N/C

sin(theta) = 3/5
cos(theta) = 4/5

E2x = E2 * sin(theta)
E2x = 1.07 * 10^4 N/C * 3/5
E2x = 6420 N/C

E2y = E2 * cos(theta)
E2y = 1.07 * 10^4 N/C * 4/5
E2y = 8560 N/C

E2 = - 6420 i + 8560 j N/C

Resultant Field E =  - 6420 i - 19420 j N/C

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