Two long wires are oriented so that they are perpendicular t

Two long wires are oriented so that they are perpendicular to each other, and at their closed, they are 2d m apart. What is the magnitude of the magnetic field at point Q midway between them if the top wire carries a current of 4.0 A and the bottom one carries a current of 3.0 A? d = 2 times 10^-6 m

Solution

Here, d = 2 x 10^-6 m.

Further, the magnitude of magnetic field due to current 4.0 A is -
B = (2.0 x 10^-7 × 4.0) / (1.0 x 10^-6) = 0.80 T

Again the magnitude of magnetic field due to current 3.0 A is -

B = (2.0 x 10^-7 × 3.0) / (1.0 x 10^-6) = 0.60 T

These are vector fields, however; to add, we have to do so vectorially.

Since both fields are perpendicular, and both sides of a right triangle, then use Pythagoras\' theorem to find the hypotenuse, which gives the magnitude of the resultant vector,

sqrt[0.80^2 + 0.60^2] = 1.0 T