A wire of length `10cm` is bent into an arc of a circle such that it subtends an angle of 1 radian at the centre. If a current of `1A` is passed through the wire, the magnetic induction at the centre of the circle will be

Options

A. `6.284xx10^(-6)Wb//m^(2)`
B. `4.284xx10^(-6)Wb//m^(2)`
C. `3.14xx10^(-6)Wb//m^(2)`
D. `1.57xx10^(-6)Wb//m^(2)`

Answer

A

Explanation

`R= 0.1m,`
`theta 120^(@) =(2pi)/(3) ` radian ` therefore l = Arc AB= R theta`
`therefore l =(2pi)/(3) xx10^(-1) m`
and `B =(mu_(0))/(4pi)(Il)/(R^(2))=(10^(-7)xx3xx2pi xx10^(-1))/(3xx 10^(-2))= 2xx3.142xx10^(-6)`
`therefore B =6.284xx10^(-6) Wb//m^(2)`
Note: We can use `B' ((theta)/(2pi))B=((2pi)/(3xx2pi))B=B/3`