Electricity and Magnetism

Magnetic Flux, Induction, and Ampere's Circuital Law

Ampere's law (Quantitative)

         

The wire loop PQRSP PQRSP formed by joining two semicircular wires of radius R1=2 cm R_1 = 2 \text{ cm} and R2=4 cm R_2 = 4 \text{ cm} carries a current of I=32 mA, I = 32 \text{ mA}, as shown in the figure above. Find the magnitude of the magnetic field at the center C. C.

The magnetic constant is μ0=4π×107 H/m. \mu_0 = 4 \pi \times 10^{-7} \text{ H/m}.

The above figure shows two stationary and infinitely long bent wires PQR PQR and STU STU lying on the xyxy-plane, each carrying a current of I=40 mA. I= 40 \text{ mA}. Find the magnitude of the magnetic filed at the origin O.O.

Assume OQ=OT=a=2 cm. OQ = OT = a = 2 \text{ cm}.
The magnetic constant is μ0=4π×107 H/m. \mu_0 = 4 \pi \times 10^{-7} \text{ H/m}.

A red wire ABCDEABCDE is bent, as shown in the figure above. The wire carries a current of I=160 mA, I = 160 \text{ mA}, and the radius of the bent coil BCD BCD is r=5 cm. r = 5 \text{ cm}. If the angle BOD \angle BOD is θ=π4 \theta = \frac{\pi}{4} , what is the magnitude of the magnetic field at the center O? O?

A red wire ABCDEF ABCDEF is bent, as shown in the figure above, carrying a current of I=54 mA. I = 54 \text{ mA}. The radius of the smaller arc ABC ABC is r1=r=3 cm r_1 = r = 3 \text{ cm} and that of the bigger arc is r2=2r. r_2 = 2r. If the angle θ \theta in the figure is given by θ=60=π3, \theta = 60^\circ = \frac{ \pi}{3} , what is the magnitude of the magnetic field at the center O? O?

The magnetic constant is mu0=4π×107 H/m. mu_0 = 4 \pi \times 10^{-7} \text{ H/m}.

A worker that maintains trolleys has to twist one part of the wiring in order to tighten up the wires. He knows that a direct current that goes through wires induces magnetic field and he wants to minimize the magnetic field in the loop to avoid any side effects.

The worker can twist the wire in two ways shown in the picture above. If the radius of the loop is rr, and the magnetic field strength at a distance rr from a straight wire was H0=10 A/mH_0 = 10~\mbox{A/m}, what is the difference between the magnetic field strength in the middle of the loop in the case a) and b) in A/m?

Details and assumptions

  • Your answer should be the absolute value of the difference between the fields.
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