Question

Point charges q1 and q2 are separated by a distance of 60 cm along a horizontal axis. The magnitude of q1 is 3 times the magnitude of q2 . At which point a on the axis is the electric field zero?

Answer 1

d = distance between the two point charges = 60 cm = 0.60 m

r = distance of the location of point "a" where the electric field is zero from charge
`q_(1)` between the two charges.

`q_(1)` = magnitude of charge on one charge

`q_(2)` = magnitude of charge on other charge

`q_(1)` = 3
`q_(2)`

`E_(1)` = Electric field by charge
`q_(1)` at point "a"

`E_(2)` = Electric field by charge
`q_(2)` at point "a"

Electric field by charge
`q_(1)` at point "a" is given as

`E_(1)` = k
`q_(1)` /r²

Electric field by charge
`q_(2)` at point "a" is given as

`E_(2)` = k
`q_(2)` /(d-r)²

For the electric field to be zero at point "a"

`E_(2)` =
`E_(1)`

k
`q_(2)` /(d-r)² = k
`q_(1)` /r²

`q_(2)` /(d-r)² = 3
`q_(2)` /r²

1/(0.60 - r)² = 3 /r²

r = 0.38 m

r = 38 cm