# Magnetic Fields in a Conducting Wire

7. A conducting metal rod 1.0 cm in diameter carries 500-A current distributed uniformly over its cross section. Using Ampere's law (a) find the magnetic field strength 0.25 cm from its axis (b) Find the B field strength at the rod's surface. (c) Find the B field at a distance 10-cm away from the center.

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Reading: Ampere's law

The magnetic field at a point due to a axially symmetric current distribution can be given by using Ampere's law.

According to this law the line integral (Product of field and length in same direction) of the magnetic field is equal to the current within the loop. Mathematically this can be written as

âˆ®â–’ã€–B âƒ—.(dl) âƒ— ã€—=Î¼_0 I

here gives the product of the length element dl (circumference) of the loop and the component of the magnetic field along the loop.

If the current is distribution is circularly uniform, the circular loop for which the magnetic field at all points equal in magnitude and parallel to it then âˆ®â–’ã€–B âƒ—.(dl) âƒ— ã€— is ...

#### Solution Summary

This solution contains step-by-step calculations to determine the field inside, outside and at the surface of a wire carrying uniform current distribution.