11.7 Applications of magnetic forces and fields  (Page 6/11)

A uniform magnetic field of magnitude $B$ is directed parallel to the z -axis. A proton enters the field with a velocity $\overrightarrow{v}=(4\widehat{j}+3\widehat{k})\times {10}^6\text{m/s}$ and travels in a helical path with a radius of 5.0 cm. (a) What is the value of $B$ ? (b) What is the time required for one trip around the helix? (c) Where is the proton $5.0\times {10}^{\mathrm{-7}}\text{s}$ after entering the field?

An electron moving at $5.0\times {10}^6\text{m/s}$ enters a magnetic field that makes a ${75}^{\text{o}}$ angle with the x -axis of magnitude 0.20 T. Calculate the (a) pitch and (b) radius of the trajectory.

(a) A 0.750-m-long section of cable carrying current to a car starter motor makes an angle of 60º with Earth’s $5.5\times {10}^{\mathrm{-5}}\text{T}$ field. What is the current when the wire experiences a force of $7.0\times {10}^{\mathrm{-3}}\text{N}?$ (b) If you run the wire between the poles of a strong horseshoe magnet, subjecting 5.00 cm of it to a 1.75-T field, what force is exerted on this segment of wire?

(a) What is the angle between a wire carrying an 8.00-A current and the 1.20-T field it is in if 50.0 cm of the wire experiences a magnetic force of 2.40 N? (b) What is the force on the wire if it is rotated to make an angle of 90º with the field?

A 1.0-m-long segment of wire lies along the x -axis and carries a current of 2.0 A in the positive x -direction. Around the wire is the magnetic field of $\left(3.0\widehat{i}\times 4.0\widehat{k}\right)\times {10}^{\mathrm{-3}}\text{T}.$ Find the magnetic force on this segment.

A 5.0-m section of a long, straight wire carries a current of 10 A while in a uniform magnetic field of magnitude $8.0\times {10}^{\mathrm{-3}}\text{T}.$ Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is (a) 45°; (b) 90°; (c) 0°; or (d) 180°.

An electromagnet produces a magnetic field of magnitude 1.5 T throughout a cylindrical region of radius 6.0 cm. A straight wire carrying a current of 25 A passes through the field as shown in the accompanying figure. What is the magnetic force on the wire?

The current loop shown in the accompanying figure lies in the plane of the page, as does the magnetic field. Determine the net force and the net torque on the loop if I = 10 A and B = 1.5 T.

A circular coil of radius 5.0 cm is wound with five turns and carries a current of 5.0 A. If the coil is placed in a uniform magnetic field of strength 5.0 T, what is the maximum torque on it?

A circular coil of wire of radius 5.0 cm has 20 turns and carries a current of 2.0 A. The coil lies in a magnetic field of magnitude 0.50 T that is directed parallel to the plane of the coil. (a) What is the magnetic dipole moment of the coil? (b) What is the torque on the coil?

A current-carrying coil in a magnetic field experiences a torque that is 75% of the maximum possible torque. What is the angle between the magnetic field and the normal to the plane of the coil?

A 4.0-cm by 6.0-cm rectangular current loop carries a current of 10 A. What is the magnetic dipole moment of the loop?

A circular coil with 200 turns has a radius of 2.0 cm. (a) What current through the coil results in a magnetic dipole moment of 3.0 Am ² ? (b) What is the maximum torque that the coil will experience in a uniform field of strength $5.0\times {10}^{\mathrm{-2}}\text{T}?$ (c) If the angle between μ and B is 45°, what is the magnitude of the torque on the coil? (d) What is the magnetic potential energy of coil for this orientation?