The two wires shown in Figure P19.38 carry currents of 5.00 A in opposite direct

Question

The two wires shown in Figure P19.38 carry currents of 5.00 A in opposite directions and are separated by 10.0 cm. Find the direction and magnitude of the net magnetic field at the following locations.

9. Consider arrangement of two long current-carrying wires given in the problem below.

(a) Determine the magnitude and direction (up, down, left, right, into or out of the page) of the magnetic field created by current flowing through the right wire at the location of the left wire.

(b) Next, determine the magnitude and direction (up, down, left, right, into or out of the page) of the force per unit length exerted upon the left wire by the right wire’s magnetic field.

(c) Is the left wire attracted toor repelled by the right wire, or does the right wire exert no force on the left wire?

Explanation / Answer

(i)Magnetic field at point P1

The net magnetic field at a point P1 which is at a distance of 10 cm is given by

Bnet = -B1 + B2­

        = -[µ0 I / 2 (2d)] + -[µ0 I / 2 (d)]

But, µ0 = 4 x 10-7 Henry/m

        d = 0.1 m

       I = 5 amp

Substituting these values in equation (1), we obtain B = 5 x 10-6 Tesla (out)

Outside magnetic field is denoted as + and inside as –

(ii)Magnetic field at point P2

The net magnetic field at a point P2 which is at a distance of 10 cm is given by

Bnet = B1 - B2­

        = [µ0 I / 2 (2d)] + -[µ0 I / 2 (3d)]

But, µ0 = 4 x 10-7 Henry/m

d = 0.1 m

       I = 5 amp

Substituting these values in equation (1), we obtain B = 1.67 x 10-6 Tesla (out)

Outside magnetic field is denoted as + and inside as -

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