Consider a current carrying wire shown in the figure. If the radius of the curved part of the wire is R and the linear parts are assumed to be very long, then the magnetic induction of the field at the point O is

Options

A. `(mu_(0))/(4pi) (i)/(R )(2 + pi)`
B. `(mu_(0)i)/(2pi R)`
C. `(mu_(0))/(2) (i)/(R )`
D. `(mu_(0))/(4) (i)/(R )`

Answer

A

Explanation

Magnetic field at point O = Magnetic field due to wire 1 + Magnetic field due to semi-circle + Magnetic field due to wire 2

`:. B_("at O") = (mu_(0)i)/(4pi R) + (mu_(0)i)/(4R) + (mu_(0)i)/(4pi R) = (mu_(0)i)/(4pi R) (2 + pi)`