Question

A +1 C charge is placed at position x=-2m, while a 2C charge is placed at position x=3m

a.) Find the net electric field (magnitude and direction) at the origin

b.) Find the net electric field (magnitude and direction) at (x,y)=(0,2m)

Show all work!

Answer 1

(A) due to point charge, E = k q / r^2

E = due to 1C + due to 2C

E = (9 x 10^9 x 1) / (2^2) - (9 x 10^9 x 2)/3^2

E = 250 x 10^6 N/C .....Ans

to the right

(B) In vector form,

E = (k q / |r|^3) (r)

q1 = 1 C

r1 = 2i + 2j |r1| = sqrt(2^2 + 2^2) = 2.828

E1 = (9 x 10^9 x 1 / 2.828^3) (2i + 2j)

E1 = (795.5 x 10^6 i) + (795.5 x 10^6 )j

q2 = 2 C

r2 = - 3 i + 2j |r2| = 3.606 m

E2 = (-1152 x 10^6)i + (768 x 10^6)j

E = E1 + E2 = - 356.5 x 10^6 i + 1563 x 10^6 j

magnitdue = sqrt(365.5^2 + 1563^2)

= 1605 x 10^6 N/C ......Ans

direction= 180 - tan^-1(1563 / 356.5)

= 103 deg