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Two parallel infinite line charges with ...

Two parallel infinite line charges with linear charge densities `+lambda C//m` and `-lambda` C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

A

Zero

B

`(2lambda)/(piepsilon_(0)R)N//C`

C

`(lambda)/(piepsilon_(0)R)N//C`

D

`(lambda)/(2piepsilon_(0)R)N//C`

Text Solution

Verified by Experts

The correct Answer is:
C

Electric field due to line charge(1)
`vecE_(1)=(lambda)/(2piepsilon_(0)R)hatiN//C`
electric field due to line charge (2).
`vecE_(2)=(lambda)/(2piepsilon_(0)R)hatiN//C`
`E_("net")=vecE_(1)+vecE_(2)`
`=(lambda)/(2piepsilon_(0)R)hati+(lambda)/(2piepsilon_(0)R)hati`
`=(lambda)/(piepsilon_(0)R)hatiN//C`
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