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# Magnetic Flux, Induction, and Ampere's Circuital Law

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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