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The figure shows two identical long stra...


The figure shows two identical long straight metal wires, A and B placed parallel to z-axis the cross sectional radius of each wire is R and the separation of the two wires is `Dgt gtR`. The electric potential at a perpendicular distance `rgtR` from a long straight wire due to that wire is given by `V=-kln((r)/(R))` where `k` is a positive constant. the wires carry charges `+Q` and `-Q` per unit length respectively. Then
Q. Consider a point P on the x-axis. The electric field at P is given by:

A

`vecE=((k)/(D-r_(p))-(k)/(r_(p)))hati`

B

`vecE=(k)/(2)((1)/(r_(p))+(k)/(D-r_(p)))hati`

C

`vecE=((k)/(r_(p))+(k)/(D-r_(p)))hati`

D

`vecE=((k)/(r_(p))-(k)/(D-r_(p)))hati`

Text Solution

Verified by Experts

The correct Answer is:
A
`E=(k)/(r)` in radial direction
At point p, `overline(E)_(1)=(k)/(r_(p))hati`
`overline(E_(2))=(k)/(D-r_(p))hati`
`because` by susperposition `overline(E)_(p)=overline(E)_(1)+overline(E_(2))`
`=((k)/(r_(p))+(k)/(D-r_(p)))hati`
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