A very long line of charge with charge per unit length +8.00 μC/m is on the x-axis and its midpoint is at x = 0. A second very long line of charge with charge per unit length -6.00 μC/m is parallel to the x-axis at y = 10.

(a) What is the magnitude of the net electric field at point y2 = 0.200 m on the y-axis?

(b) What is the magnitude of the net electric field at point y3 = 0.616 m on the y-axis?

a. E=6.5*10^{5}N/C

b. E=-4.7*10^{4}N/C

Explanation:

We can use the result of applying the Gauss theorem to a infinite line of charge

with r the perpendicular distance to the line of charge. The total field will be the sum of the contribution to the field by each line of charge.

E=E1+E2

we have

+8.00 μC/m

-6.00 μC/m

y=1m

(a) y2=0.2m

(b) y3=0.616m

In this case the field is directed toward the line of charge placed in y=1m

a and c

explanation:

both a and c are correct answers to my knowledge, it's been a bit since i've done anything related to magnetic fields, but it should be right.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west