In the figure cross-section has been shown of a long thin ribbon of width w that is carrying a uniformly distributed total current into the page. We have to calculate the magnitude and the direction of the magnetic field at a point P in the plane of the ribbon at a distance d from its edge.

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We imagine the ribbon to be comprising of many, long, thin, parallel wires each of thickness . The current in each such wire will be . As the current is entering into the plane of page, using the right-hand rule, we note that the direction of the magnetic field at P will be in the direction of the unit vector , and the magnetic field will be uniform circles around each thin wire.

The magnetic field at P due to a wire element at distance from the right-hand edge will be

Therefore, the magnetic field at P due to the ribbon with current will be given by the integral

For calculating the above integral, we make the substitution

We get