Question

Three point charges lie in a straight line along the y-axis. A charge of q1 = -10.00 µC is at y = 6.40 m, and a charge of q2 = -7.70 µC is at y = -3.60 m. The net electric force on the third point charge is zero. Where is this charge located?

Answer 1

y coordinate where field is zero is 1.1 m

Step-by-step explanation:

given data

charge q1 = -10.00 µC

y = 6.40 m,

charge q2 = -7.70 µC

y = -3.60 m

solution

we know that here Electric field E that is express as

Electric field E =
`(kQ)/(r^2)` ..............................1

and

Distance between charges will be

Distance between charges = 6.40 - (-3.60) = 10 m

so here neutral point P is at distance d from q1

so it is distance (10 - d) from q2.

so here

Field from q1 at P =
`(k(-10 * 10^(-6)))/(d^2)`

and

Field from q2 at P =
`(k(-7.70 * 10^(-6)))/((10-d)^2)`

so here field is in opposite directions and the resultant field = 0

so

`(k(-10 * 10^(-6)))/(d^2) = (k(-7.70 * 10^(-6)))/((10-d)^2)`

`(10)/(d^2) = (7.70)/((10-d)^2)`

d = 5.326242 m

so y coordinate where field is zero is 6.40 - 5.32 = 1.1 m