The magnitude of the force vector acting on a unit length of a thin wire carrying a current `I=8 A` at a point O, if the wire is bent as shown in the figure with a radius `R=10 pi` cm is

Options

A. 64 `mu`N/m
B. 32 `mu`N/m
C. 20 `mu`N/m
D. 100 `mu`N/m

Answer

A

Explanation

Given, current flowing through wire, `I=8A` and radius of circular wire,
`R=10 pi` cm `=10 pi xx10^(-2)` m
According to the question,

`:'` Magnetic field produced by semi-circular current carrying thin wire at centre O.
`B=(mu_(0) I)/(4 R)`
Putting the given values, we get
`B=(4pi xx10^(-7) xx8)/(4xx10pi xx10^(-2))`
`implies B=8xx10^(-6) T`
`:.` Magnitude of the force on thin wire per unit length.
`F-IB`
Putting the given values,
`=8xx8xx10^(-6)`
`=64xx10^(-6) N//m=64 mu N//m`