Magnetic Flux, Induction, and Ampere's Circuital Law
Consider an elliptical shaped single wire loop having a major axis of \(H=40.0 \text{ cm}\) and a minor axis of \(L=30.0 \text{ cm},\) which is in a uniform magnetic field of \(6.00 \times 10^{-4} \text{ T}\) directed toward the left of the screen. The wire loop lies in the plane of the screen and carries a clockwise current of \(6.00 \text{ A}.\) What is the approximate magnitude of the torque on the coil?
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 rectangular coil having dimensions of \(3.0 \text{ cm}\) by \(7.0 \text{ cm},\) which is placed in a uniform magnetic field of magnitude \(8.00 \text{ T}.\) If the maximum torque exerted on it by the magnetic field is \(0.25 \text{ N}\cdot\text{m},\) what is the approximate current in the coil?
Suppose that a circular single wire loop of diameter \(12.0 \text{ cm}\) is placed in a uniform magnetic field of \(4.00 \text{ mT}.\) If the wire loop carries a current of \(6.00 \text{ A},\) what is the approximate maximum torque on the wire loop?
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 \(1.70 \times 10^{-8} \,\Omega \cdot \text{m}.\)