Two very long, straight, parallel wires carry currents that are directed perpend

Question

Two very long, straight, parallel wires carry currents that are directed perpendicular to the page as shown in Figure P30.9. Wire 1 carries a current I_1 into the page (in the -z direction) and passes through the x axis at x = +a. Wire 2 passes through the x axis at x = -2a and carries an unknown current I_2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 2 mu_0 I_1/( 2pi a ). The current I_2 can have either of two possible values. Find the value of I_2 with the smaller magnitude, stating it in terms of I_1 and giving its direction. (Use I_1 for I_1 as necessary.) I_2 = Find the other possible value of I_2. (Use I_1 for I_1 as necessary.) I_2 =

Explanation / Answer

given:

current-carrying wires has the magnitude 2µ0 I1 / ( 2a )

fro the Amperes law,

1. B = (0.25*µ0/pi) *2*I1/a -(0.25*µ0/pi) *2*I2/(2a) =2*µ0*I1/(2a );

or; 0.25 *2*I1 -0.25*I2/ =I1;

or, 2*I1 -I2 =4*I1; I2=-2*I_1;

2.B = (0.25*µ0/pi) *2*I1/a -(0.25*µ0/pi) *2*I2/(2a) =-2*µ0*I1/(2a );

or; 0.25 *2*I1 -0.25*I2/ =-I1;

or; 2*I1 -I2 =-4*I1; I2=6*I_1;

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