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A level physics help!!!! Electric fields

Hi
Could someone please help me with part b of this problem?

Calculate
a) the force between 2 charges of +1.4nC and +1.6nC on point conductors 40cm apart in air.
b)What size of charge on a third point conductor placed midway between the first two conductors would result in doubling of the magnitude of the force on the 1.4nC charge?

My answer for the first part was 1.2586x10^-7

Thanks in advance!!!
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Original post by Skipper12345
Hi
Could someone please help me with part b of this problem?

Calculate
a) the force between 2 charges of +1.4nC and +1.6nC on point conductors 40cm apart in air.
b)What size of charge on a third point conductor placed midway between the first two conductors would result in doubling of the magnitude of the force on the 1.4nC charge?

My answer for the first part was 1.2586x10^-7

Thanks in advance!!!

Hi,
you know the force in part a) is F1=q1q24πϵor2x \vec{F_1} = \frac{-q_1q_2}{4\pi\epsilon_o r^2}\vec{x}
So you want this force to be doubled when we introduce a charge q3 between q1 and q2

2F=2q1q24πϵor2x=q1q24πϵor2xq1q34πϵo(r/2)2x 2\vec{F} = -2\frac{q_1q_2}{4\pi\epsilon_o r^2}\vec{x}= -\frac{q_1q_2}{4\pi\epsilon_o r^2}\vec{x}-\frac{q_1q_3}{4\pi\epsilon_o (r/2)^2}\vec{x}

now you can solve this for q3q_3
(edited 7 years ago)

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