Two long, straight, parallel wires carry currents that are directed perpendicula

Question

Two long, straight, parallel wires carry currents that are directed perpendicular to the page as shown in the figure. Wire 1 carries a current I_1 into the page (in the negative 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/(2 pi a). The current I_2 can have either of two possible values. (a) Find the value of I_2 with the smaller magnitude, stating it in terms of I_1 and giving its direction. I_2 = (b) Find the other possible value of I_2. I_2 =

Explanation / Answer

The magnetic field at the origin will be:

B = B1 + B2

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

but B = 2 u0 I1/(2 pi a)

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

2 I1 = I1 + I2/2

I2 = 2I1

Hence, I2 = 2 I1, out of the page.

b)For this, B = B2 - B1

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

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

2 I1 = I2/2 - I1

I2 = 6 I1

Hence, I2 = 6 I1 ; into the page.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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