91Ó°ÊÓ

A solenoid has 4850 turns per meter and radius \(3.3 \mathrm{cm}\) The magnetic field inside has magnitude 0.24 T. What is the current in the solenoid?

Four long parallel wires pass through the corners of a square with side $0.10 \mathrm{m}\(. All four wires carry the same magnitude of current \)I=10.0 \mathrm{A}\( in the directions indicated. Find the magnetic field at point \)R,$ the midpoint of the left side of the square.

The intrinsic magnetic dipole moment of the electron has magnitude $9.3 \times 10^{-24} \mathrm{A} \cdot \mathrm{m}^{2} .$ In other words, the electron acts as though it were a tiny current loop with $N I A=9.3 \times 10^{-24} \mathrm{A} \cdot \mathrm{m}^{2} .$ What is the maximum torque on an electron due to its intrinsic dipole moment in a \(1.0-T\) magnetic field?

An electromagnet is made by inserting a soft iron core into a solenoid. The solenoid has 1800 turns, radius \(2.0 \mathrm{cm},\) and length $15 \mathrm{cm} .\( When \)2.0 \mathrm{A}$ of current flows through the solenoid, the magnetic field inside the iron core has magnitude 0.42 T. What is the relative permeability \(\overline{K_{\mathrm{B}}}\) of the iron core? (See Section 19.10 for the definition of \(\boldsymbol{K}_{\mathbf{B}} .\) )

In a simple model, the electron in a hydrogen atom orbits the proton at a radius of \(53 \mathrm{pm}\) and at a constant speed of $2.2 \times 10^{6} \mathrm{m} / \mathrm{s} .$ The orbital motion of the electron gives it an orbital magnetic dipole moment. (a) What is the current \(I\) in this current loop? [Hint: How long does it take the electron to make one revolution?] (b) What is the orbital dipole moment IA? (c) Compare the orbital dipole moment with the intrinsic magnetic dipole moment of the electron $\left(9.3 \times 10^{-24} \mathrm{A} \cdot \mathrm{m}^{2}\right)$

You want to build a cyclotron to accelerate protons to a speed of $3.0 \times 10^{7} \mathrm{m} / \mathrm{s} .$ The largest magnetic field strength you can attain is 1.5 T. What must be the minimum radius of the dees in your cyclotron? Show how your answer comes from Newton's second law.

A long straight wire carries a \(4.70-\) A current in the positive \(x\) -direction. At a particular instant, an electron moving at $1.00 \times 10^{7} \mathrm{m} / \mathrm{s}\( in the positive \)y\( -direction is \)0.120 \mathrm{m}$ from the wire. Determine the magnetic force on the electron at this instant. Sce the figure with Problem \(65 .\)

A uniform magnetic field of \(0.50 \mathrm{T}\) is directed to the north. At some instant, a particle with charge \(+0.020 \mu \mathrm{C}\) is moving with velocity \(2.0 \mathrm{m} / \mathrm{s}\) in a direction \(30^{\circ}\) north of east. (a) What is the magnitude of the magnetic force on the charged particle? (b) What is the direction of the magnetic force?

(a) A proton moves with uniform circular motion in a magnetic field of magnitude 0.80 T. At what frequency \(f\) does it circulate? (b) Repeat for an electron.