The wires A and B are of lengths 40 cm and 30 cm. A is bent into a circle of radius r and b into an are of radius r. A current `i_(1) ` is passed through A and ` i_(2)` through B. To have the same magnetic inductions at the centre, the ratio of `i_(1): i_(2)` is

Options

A. `3:4`
B. `3:5`
C. `2:3`
D. `4:3`

Answer

A

Explanation

Magnetic field induction for wire A,
`B_(1)=(mu_(0)i_(1))/(2r)`
`l_(1)=2pir`
`r=40/2pi`
For wire B,npir=30
Circumference=Length
`npir=(30)/(40/2pi)`
`=3/2pi`
`B_(1)=(mu_(0))/(4pi)(i_(2)/4)theta`
`B_(1)=B_(2)``implies(mu_(0)i_(1))/(2r)=(mu_(0))/(4pi)(i_(2)/(r))theta`
`thereforei_(1)/i_(2)=3/4`