Magnetic fields are wondrous things, bound by geometric relationships to the moving currents that generate them. Learn these links and the things they govern, from transformers to electric motors.

**Note:** The area of an ellipse is \(A=\pi ab,\) where \(a\) and \(b\) are, respectively, the semi-major and semi-minor axes of the ellipse.

Suppose that a circular path of radius \(r=5.10 \times 10^{-11} \text{ m},\) on which an electron moves with speed \(2.40 \times 10^6 \text{ m/s},\) lies in a uniform magnetic field of magnitude \(B=7.40 \text{ mT}.\) If we treat the circular path as a current loop, what is the approximate maximum possible magnitude of the torque produced on the loop by the magnetic field?

**Assumptions and Details**

- The elementary charge is \(1.60 \times 10^{-19} \text{ C}.\)

Consider a single wire loop in the shape of square made from a copper wire with length \(8.0 \text{ m}\) and cross-sectional area \(1.2 \times 10^{-4} \text{ m}^2.\) If it is connected to a potential difference of \(0.10 \text{ V}\) and then placed in a uniform magnetic field of magnitude \(0.50 \text{ T},\) what is the approximate maximum torque that can act on it?

The resistivity of copper is \(1.70 \times 10^{-8} \,\Omega \cdot \text{m}.\)

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