A steady current I flows through a wire with one end at O and the other end extending upto infinity as shown in the figure. The magnetic field at a point P, located at a distance d from O is

Options

A. `(mu_0 I)/(4pi d cos alpha) (1 - sin alpha )`
B. `(mu_0 I)/(2pi d cos alpha) (1 - sin alpha )`
C. `(mu_0 I)/(4 pi d)`
D. `(mu_0 I)/( 4pi d sin alpha) (1 - sin alpha)`

Answer

D

Explanation

From result of field of a long wire , we have
`beta = (mu_0)/(4pi ) xx I/r xx (sin theta_1 - sin theta_2)`
Here , ` r = d sin alpha `
` sin theta_1 = sin 90^@ = 1`
` sin theta_2 = sin (90 - alpha) = cos alpha`
so, `beta = (mu_0 I)/(4pi d sin alpha) (1 - cos alpha)`