Question

A 4.3 µC (q₁) and a -2.5 µC (q₂) charge are placed 1.6 cm apart. At what points along the line joining them do the following things occur? (List all answers as positive numbers.)

(a) the electric field is zero

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

(b) the potential is zero

1. ---------------

2.---------------

Answer 1

given

4.3 µC = q₁ and

- 2.5 µC = q₂ charge are placed

d = 1.6 cm

= 0.016 m  

a )

the electric field is zero

[ k x 4.3 x 10^-6 / ( 0.016 + x )² ] - [ k x 2.5 x 10^-6 / x² ] = 0

[ k x 4.3 / ( 0.016 + x )² ] - [ k x 2.5 / x² ] = 0

[ 4.3 / ( 0.016 + x )² ] - [ 2.5 / x² ] = 0

( 0.016 / x ) + 1 = ( 4.3/2.5 )^1/2  

( 0.016 / x ) + 1 = 1.311

0.016 / x = 0.311

x = 0.016 / 0.311

x = 0.05144 m

x = 5.144 cm ( to the left of negative charge )

b )

the potential is zero

( k x -2.5 / y ) + ( k x 4.3 / (0.016 - y ) ) = 0

0.016 / y = 4.3/2.5

0.016 / y = 1.72

y = 0.016 / 1.72

y = 9.3 x 10^-3 m

or

y = 9.3 mm ( to the right of negative charge )