question_answer

A straight wire of diameter 0.5 mm carrying a current of 1A is replaced by another wire of 1 mm diameter carrying the same current. The strength of magnetic field far away is :

A)  unchanged

B)  quarter of its earlier value

C)  half of the earlier value

D)  twice the earlier value

Correct Answer: A

Solution :

                The strength of magnetic field at the observation point due to a straight current carrying wire is \[B=\frac{{{\mu }_{0}}i}{2\pi r}\]where r= distance of point from the wire. It is obvious from the relation that magnetic field does not depend on diameter of the wire, so it remains unchanged. NOTE: Since \[B\propto \frac{1}{r}\]. so B-r graph for an infinitely long straight wire is a rectangular hyperbola (as shown in figure).