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Chapter 26: Problem 72

A circular wire loop of radius \(15 \mathrm{cm}\) and negligible carries a 2.0 -A current. Use suitable approximations to find the magnetic field of this loop (a) in the loop plane, 1.0 mm outside center

Short Answer

Expert verified
The magnetic field in the plane of the loop at the center is \(8.37 \times 10^{-6} \, T\), while it is \(0 \, T \) at a point 1.0 mm outside the center in the plane.

Step by step solution

01

Gather all known values

The current \(I\) in the wire loop is given as \(2.0 \, A\), the radius \(r\) of the loop is \(15 \, cm = 0.15 \, m\), and the distance \(d\) from the loop is given as \(1.0 \, mm = 0.001 \, m\).
02

Apply Biot-Savart Law

Biot-Savart Law relates the magnetic field \(B\) to the current \(I\), the distance \(r\) from the wire, and the constant \(\mu_0 = 4\pi \times 10^{-7} \frac{Tm}{A}\). For a circular loop, the Biot-Savart Law simplifies to: \(B = \frac{\mu_0 I}{2R}\),, where \(R\) is the radius of loop
03

Calculate the magnetic field \(B\)

By substituting given values into the simplified Biot-Savart law, calculate the magnetic field \(B = \frac{4\pi \times 10^{-7} \times 2.0}{2 \times 0.15} = 8.37 \times 10^{-6} \, T\)
04

Consider point outside the loop

The magnetic field at a distance \(d\) from the center along the plane of the loop will be zero since magnetic field lines due to the current loops are circular and at any point on the plane of the loop outside it, the magnetic field due to current at different points cancel out due to symmetrical distribution of currents around the point. Hence, \(B_{outside} = 0\)

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Most popular questions from this chapter

If a current is passed through an unstretched spring, will the spring contract or expand? Explain.

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