Question

Two point charges q_A = 3 μC and q_B = −3 μC are located 20 cm apart in vacuum.

1. What is the electric field at the midpoint O of the line AB joining the two charges?
2. If a negative test charge of magnitude 1.5 × 10⁻⁹ C is placed at this point, what is the force experienced by the test charge?

Answer 1

(a)

 

Electric fields at O due to the charges at A and B are:

`E_(OA) = E_(OB) = 1/(4 pi ε_0) q/r^2`

= `9 xx 10^9 xx (3 xx 10^-6 C)/((20xx 10^-2 m)/2)^2`

= `(27 xx 10^3 C)/((10 xx 10^-2  m)^2`

= `(27 xx 10^3 C)/(0.1  m)^2`

= `(27 xx 10^3 C)/(10^-2  m^2)`
or E_OA = E_OB = 27 × 10⁵ NC⁻¹

Being in the same direction results in a net electric field at the midpoint O, which is:

E = E_OA + E_OB

= 2E_OB

= 2 × 27 × 10⁵
or E = 5.4 × 10⁶ N C⁻¹ directed along OB.

(b) A force acts onto the test charge when it is put at point O, with q₀ = −1.5 × 10⁻⁹ C.

F = q₀E

= 1.5 × 10⁻⁹ × 5.4 × 10⁶

= 8.1 × 10⁻³ N

A long OA, which is opposite to E.