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Q.45

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

Find an expression for the magnetic field strength at the center (point P) of the circular arc in

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Step by Step Solution

Step.1. Given information 

We should find an expression for the magnetic field strength at the center (point P) of the circular arc in

Step.2 solution 

A current-carrying wire produces a magnetic field the Biot-Savart law enables us to calculate the magnetic field at any point where the magnetic field due to the segment of current-carryinjg wire is given by equation

(1)

The two straight wires are parallel to the point P, so both wires apply zero magnetic fields at point P in this case, the magnetic field at point P is due to the arc wire. The arc wire apply a perpendicular magnetic field at point P, so the magnetic field due to the arc is

(2)

At very small segments the angle is very small where and from the given figure, segment is

Where r is the radius of the arc. Now, we substitute the expression into equation to get

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