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Figure shows two rods each of length L p...

Figure shows two rods each of length L placed side by side, with their facing ends separated by a distance a. Charges +q, -q reside on the rods as shown. Calculate the electric force on the rod A due to the rod B. Discuss the cases when `lgtgta`, `agtgt1`

Text Solution

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The force on the rod A due to the charge +q of the rod B
=- q^2/(4pi eplsilon_0(l+a0^2)+q^2/(4 pi eplsilon_0 a^2)`
towards right. The force on this rod due to the charge -q.
`q^2/(4 pi eplsilon_0(2l+a)^2) - q^2/(4 pi epsilon_0(l+a)^2)`
towards right.
The resultan force on the rod is
`F= q^2 /(4 pi epsilon_0) [1/a^2-2/((l+a)^2)+1/((2l+a)^2)`]` towards right.
If `lgtgta`, the last two terms in the square bracket are negligible as compared to the first term. then,
`F~~q^2/(4pi epsilon_0 a^2)`
If `agtgt1`
`F=q^2/(4 pi eplsilon_0) [1/a^2-2/a^2+1/a^2]~~0`
Two neutral object placed far away exert only negligible force on each other but when they are placed closer they may exert appreciable force.
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