A wire carrying current `I` has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicicular portion of radius `R` is lying in `Y-Z` plane. Magnetic field at point `O` is

Options

A. `vecB = - (mu_0)/(4pi ) I/R ( pi hati + 2 hatk )`
B. `vecB = (mu_0I)/(4pi R) (pi hati - 2 hatk)`
C. `vecB = (mu_0 I)/(4pi R) (pi hati + 2 hatk )`
D. `vecB = - (mu_0 I)/(4pi R) (pi hati - 2 hatk)`

Answer

A

Explanation

`vecB_1` = magnetic field at O due to current in parallel wires
`vecB_2` = magnetic field due to semi - circular wire
` vecB_1 = vecB_1 + vecB_2`
` = - (mu_0 i)/(2pi R) (hatk) - (mu_0 i)/(4R) (hati)`
` = - (mu_0 i)/(4pi R) (pi hati + 2hatk) `