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)/(4 pi) I/R (pi hat i - 2 hat k)`
B. `vecB =- mu_(0)/(4 pi) I/R (pi hat i + 2 hat k)`
C. `vecB = mu_(0)/(4 pi) I/R (pi hat i - 2 hat k)`
D. `vecB = mu_(0)/(4 pi) I/R ( pi hat i + 2 hat k) `

Answer

b

Explanation

Magnetic field at O due to the semicircular loop is:
`vec B_(1) = (mu_(0)I pi)/(4 pi R) (- hat i)`
Magnetic field at O due to semi-infinite long wires will be:
` vec B_(2) = 2 [(mu_(0)I)/(4 pi R)] (- hat k)`
Then, the net magnetic field at O will be :
`vecB = vec B_(1) + vec B_(2) = (mu_(0)I pi)/(4 pi R) ( - hat i ) + (mu_(0)I)/(4 pi R) ( - 2 hat k)`
` = - (mu_(0)I)/(4 pi R) (pi hat i + 2 hat k) `