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Question
Two point charges qA = 3 μC and qB = −3 μC are located 20 cm apart in vacuum.
- What is the electric field at the midpoint O of the line AB joining the two charges?
- 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?
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Solution
(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 EOA = EOB = 27 × 105 NC−1
Being in the same direction results in a net electric field at the midpoint O, which is:
E = EOA + EOB
= 2EOB
= 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.
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