Question

What is the magnetic induction of the field at the point O in a current I carrying wire that has the shape shown in the figure? The radius of the curved part of the wire is R, the linear parts are assumed to be very long.

Options

• `(mu_0"I")/(4pi"R") [2 + pi]`

• `(mu_0"I")/(4pi"R") [2 + (3pi)/2]`

• `(mu_0"I")/(4pi"R") [1 + pi/2]`

• `(mu_0"I")/(4pi"R") [1 + (3pi)/2]`

Answer 1

`(mu_0"I")/(4pi"R") [2 + (3pi)/2]`

Explanation:

Magnetic field at centre 'O'

B_O = 2 (Magnetic field dut to straight wire) + magnetic field due to circular wire

`= 2 (("M"_0"I")/(4pi"r")) + (3"M"_0"I")/(8"R")`

`therefore "B"_0 ("M"_0"I")/(4pi"R")(2 + 3/2 pi)`