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  4. 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 :

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Q. 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 :

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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).

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