Question

Suppose we have an infinitely long wire carrying a current of 3.5 A. It is bent into an L-shape extending into positive infinities along the x- and y- axes. Find the magnitude of the magnetic field at a point P with coordinates (0.4 m, 0.4 m).

B = T

Answer 1

Solution - For an infinitely long wire, B( magnetic field) at a point at distance 0.4 m

= [ U.i / 4.(pi)d ] * ( cosa + cosb )

Here i = 3.5 amperes, U is the permittivity of free space = 4(pi) * 10^-7 , d = 0.4 m

For the wire along the X-axis, angle subtended at origin = 45 degrees.

And at infinity, angle subtended = 0 degrees

Thus, B = 3.5 * 10^-7 / 0.4 * ( cos45 + cos0)

                      = 0.875 * 10^-6 * ( cos45 + cos0 )

Similarly for the wire along the Y-axis,

B = 0.87 * 10^-6 * (cos45 + cos0)

Now, we see that B due to both the wires would in the same direction, and would algebraically add up.

thus, B (total ) = 3.5 * 10^-6 * ( cos45 + cos0 )

Putting the values of cos45 = 0.707 and cos0 = 1, we get

B = 3.5 * 10^-6 * 1.707

               = 5.9745 * 10^-6 Tesla

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