Electricity and Magnetism

Magnetic Flux, Induction, and Ampere's Circuital Law

Magnetic moment

         

Consider an elliptical shaped single wire loop having a major axis of H=40.0 cmH=40.0 \text{ cm} and a minor axis of L=30.0 cm,L=30.0 \text{ cm}, which is in a uniform magnetic field of 6.00×104 T6.00 \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 A.6.00 \text{ A}. What is the approximate magnitude of the torque on the coil?

Note: The area of an ellipse is A=πab,A=\pi ab, where aa and bb are, respectively, the semi-major and semi-minor axes of the ellipse.

Suppose that a circular path of radius r=5.10×1011 m,r=5.10 \times 10^{-11} \text{ m}, on which an electron moves with speed 2.40×106 m/s,2.40 \times 10^6 \text{ m/s}, lies in a uniform magnetic field of magnitude B=7.40 mT.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 1.60×1019 C.1.60 \times 10^{-19} \text{ C}.

Consider a single rectangular coil having dimensions of 3.0 cm3.0 \text{ cm} by 7.0 cm,7.0 \text{ cm}, which is placed in a uniform magnetic field of magnitude 8.00 T.8.00 \text{ T}. If the maximum torque exerted on it by the magnetic field is 0.25 Nm,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 cm12.0 \text{ cm} is placed in a uniform magnetic field of 4.00 mT.4.00 \text{ mT}. If the wire loop carries a current of 6.00 A,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 m8.0 \text{ m} and cross-sectional area 1.2×104 m2.1.2 \times 10^{-4} \text{ m}^2. If it is connected to a potential difference of 0.10 V0.10 \text{ V} and then placed in a uniform magnetic field of magnitude 0.50 T,0.50 \text{ T}, what is the approximate maximum torque that can act on it?

The resistivity of copper is 1.70×108Ωm.1.70 \times 10^{-8} \,\Omega \cdot \text{m}.

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