# Magnetic Field Generated by a Short Current

Calculate magnetic field generated by a short current carrying segment of wire for the spot indicated in the diagram below.

. (0.5m, 0.5m)

(0,0)_____________>__________________ (1m, 0)

I= 2A

|---------------- 1m -----------------------|

https://brainmass.com/physics/biot-savart-law/magnetic-field-generated-short-current-294255

## SOLUTION This solution is **FREE** courtesy of BrainMass!

According to Biot-Savart law the magnetic field due to a current carrying segment is given by:

(1.1)

In our case we can write:

(1.2)

The directionality of the cross product is determined by the right hand rule and in this case the magnetic field points out of the page.

However:

(1.3)

And

(1.4)

Thus, equation (1.1) now becomes:

(1.5)

All that is left is to integrate between :

(1.6)

To solve the integral we use:

Therefore, equation (1.6) becomes:

(1.7)

The integrand is an even function, so we can use:

(1.8)

This is a simple integration, and we will use the fact that:

(1.9)

Back to equation (1.8) we obtain:

(1.10)

Note that when we let we regain the field for infinite wire:

What is left is to plug in the numbers:

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