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 I1 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 I2. The total magnetic field at the origin due to the current-carrying wires has the magnitude 2?0I1 / ( 2?a ). The current I2 can have either of two possible values.

(a) Find the value of I2 with the smaller magnitude, stating it in terms of I1 and giving its direction. (Use the following as necessary: I1.)
(b) Find the other possible value of I2. (Use the following as necessary: I1.)

Explanation / Answer

field due to I1 at the origin,

B1 = u0 I1 / 2 pi(a) = u0 I1 / (2 pi a) upward

and B1 + B2 = +- 2 u0 I1 / (2 pi a)

so B2 = u0 I1 / (2 pi a) upward

Or 3 u0 I1 / (2 pi a) downward

(A) for first case, current will be out of page.

u0 I2 / (2 pi (2a)) = u0 I1 / (2 pi a)

I2 = 2 I1

(B) for second case, current will be into the page.

u0 I2 / (2 pi 2a) = 3 u0 I1 / (2 pi a)

I2 = 6 I1

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.