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

A wire carrying current `I` has the shape as shown in the adjoining fi

1.	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 A. `vec(B) = (mu_(0))/(4pi) (I)/(R) (pi hat(i) + 2 hat(k))`B. `vec(B) = - (mu_(0))/(4pi) (I)/(R) (pi hat(i) - 2 hat(K))`C. `vec(B) = -(mu_(0))/(4pi) (I)/(R) (pi hat(i) + 2 hat(k))`D. `vec(B) = (mu_(0))/(4pi) (I)/(R) (pi hat(i) - 2 hat(K))`
Answer» Correct Answer - C Magnetic field due to staright wire 1 `vec(B)_(1) = (mu_(0) I)/(4pi R) [sin 90^(@) +sin 0^(@)] (-vec(k))` `=(-mu_(0)I)/(4pi R)(hatk)=vec(B)_(3)` Magnetic field due to semicircular wire 2 `B_(2)= (-mu_(0) I)/(4R) (-hat(i)) = (-mu_(0) I)/(4pi R) (pi hat(i))` Magnetic field `vec(B)` at centre, `vec(B)_(c) = vec(B)_(1) + vec(B)_(2) + vec(B)_(3)` `implies vec(B)_(c) = (-mu_(0) I)/(4pi R) (pi hat(i) + 2 hat(k))`

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