Question

<Physics problem>

Given two charges, 5Q at x = 0.0 m and 2Q at x = 2.0 mm:

Are there any points along the x-axis where E = 0? If so, find them.

What if the 2Q charge is instead -2Q? Again, find all points along the x-axis where E = 0.

Answer 1

q1 = 5Q

q2 = 2Q

q2 and q1 are of same sign ( positiv)

so the electric field E = 0 in between them

at point x E = 0

E1 = E2

k*q1/x^2 = k*q2/(d-x)^2

q1/x^2 = q2/(d-x)^2

5Q/x^2 = 2Q/(2-x)^2

5/x^2 = 2/(2-x)^2

x = 1.22 mm

----------------------------

if q2 = -2Q

so the electric field E = 0 beyond q2

at point x , E = 0

E1 = E2

k*q1/x^2 = k*q2/(x-d)^2

q1/x^2 = q2/(x-d)^2

5Q/x^2 = 2Q/(x-2)^2

5/x^2 = 2/(x-2)^2

x = 5.44 mm

DONE please check the answer. any doubts feel free to ask