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