A straight conductor of length l carrying a current I, is bent in the form of a semicircle. The magnetic field (in tesla) at the centre of the semicircle is:

Options

A. ` ( pi^(2) I)/(l)xx 10 ^(-7)`
B. ` (piI)/(l ) xx 10 ^(-7) `
C. ` (pi l)/(l^(2)) xx 10 ^(-7)`
D. ` (pi l^(2))/(l ) xx 10 ^(-7)`

Answer

A

Explanation

Radius, r `= (l)/(pi )`
Magnetic field at the centre , B `= (mu_0 I)/(4 r )`
` = (4pi xx 10 ^(-7) xx I)/(4 xx (l)/(pi )) `
` = ( pi^(2) lxx 10^(-7))/(l)`