Two long, parallel wires carry currents of I 1 = 2.70 A and I 2 = 4.65 A in the

Question

Two long, parallel wires carry currents of I1 = 2.70 A and I2 = 4.65 A in the direction indicated in the figure below. (Choose the line running from wire 1 to wire 2 as the positive x-axis and the line running upward from wire 1 as the positive y-axis.)

(a) Find the magnitude and direction of the magnetic field at a point midway between the wires (d = 20.0 cm).

(b) Find the magnitude and direction of the magnetic field at point P, located d = 20.0 cm above the wire carrying the 4.65-A current.

Explanation / Answer

Find r2 with the Pythagorean theorem. It ends up being approximately .14 meters since d=10 cm. Find B2 using (Uo I2)/(2 pi r). Then, find the components of B2. You know from the triangle you drew to find r that theta=45 degrees, and from the right hand rule that B2 points up and to the right. Once you get the x and y components, you add B1 to the x component since its vector goes to the right, also found using the right hand rule. Then you can find B from the x and y values, and use two of those components find the angle.

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