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Set 54 Problem number 1


Problem

 

A straight wire segment of length 8 meters carries a current of 8 Amps.  Find the strength of the magnetic field  at a point lying 3.2 meters from the segment, if the segment is perpendicular to a vector from the center of the segment to the point.

Solution

The magnetic field at a point P due to a short current segment, with point P lying 'at a perpendicular' to the segment, is proportional to the current and the length of the segment.

The specific value of the magnetic field is given by B=k ' (IL)/r ^ 2.

Thus

Generalized Solution

Just as the electric field strength E = k q / r^2 of a point charge q falls off as the inverse square of distance from the source q, the magnetic field B = k' (IL) / r^2 of a short charge-and-length segment IL falls of as the inverse square of its distance from the source IL.

The magnetic field is a little trickier than the electric field, since it depends not only on distance but on the orientation of the point with respect to the direction of the current I from which it arises. However

The direction of the magnetic field is found by the right-hand rule:

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