A cosmic-ray electron moves at $7.5 \times 10^6 \mathrm{~m} / \mathrm{s}$ perpendicular to Earth's magnetic field at an altitude where the field strength is $1.0 \times 10^{-5} \mathrm{~T}$. What is the radius of the circular path the electron follows?

(a) A dc power line for a light-rail system carries 1000 A at an angle of $30.0 ^ { \circ }$ to Earth’s $5.0 \times 10 ^ { - 5 } \mathrm { T }$ field. What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.

(a) A cosmic ray proton moving toward the Earth at $5.00 \times 10^{7}\ \mathrm{m} / \mathrm{s}$ experiences a magnetic force of $1.70 \times 10^{-16}\ \mathrm{N}.$ What is the strength of the magnetic field if there is a $45^{\circ}$ angle between it and the proton's velocity? Is the value obtained in part (a) consistent with the known strength of the Earth's magnetic field on its surface? Discuss.

A cosmic ray electron moves at $7.50 \times 10^{6} \mathrm{m} / \mathrm{s}$ perpendicular to the Earth’s magnetic field at an altitude where field strength is $1.00 \times 10^{-5} \mathrm{T}.$ What is the radius of the circular path the electron follows?

An alpha-particle $\left( m = 6.64 \times 10 ^ { - 27 } \mathrm { kg }, q = 3.2 \times 10 ^ { - 19 } \mathrm { C }\right )$ travels in a circular path of radius 25 cm in a uniform magnetic field of magnitude 1.5 T. (a) What is the speed of the particle? (b) What is the kinetic energy in electron-volts? (c) Through what potential difference must the particle be accelerated in order to give it this kinetic energy?

A proton and an alpha particle (charge = 2e, mass = $6.64 \times 10 ^ { - 27 }$ kg) are initially at rest, separated by $4.00 \times 10 ^ { - 15 }$ m. Find the speeds of the proton and alpha particle, respectively, at infinity.

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?

An alpha particle (the nucleus of a helium atom) has a mass of $6.64 \times 10^{-27}$ kg and a charge of +2e. What is the direction of the electric field that will balance the gravitational force on the particle?

$(a)$ A cosmic ray proton moving toward Earth at $5.00 \times 10^7 \mathrm{~m} / \mathrm{s}$ experiences a magnetic force of $1.70 \times 10^{-16} \mathrm{~N}$. What is the strength of the magnetic field if there is a $45^{\circ}$ angle between it and the proton's velocity? $(b)$ Is the value obtained in part a. consistent with the known strength of Earth's magnetic field on its surface? Discuss.

A physicist is designing a cyclotron to accelerate protons to one-tenth the speed of light. The magnetic field will have a strength of $1.5 \mathrm{~T}$. Determine $(a)$ the rotational period of the circulating protons and $(b)$ the maximum radius of the protons' orbit.

The cross section of a copper strip is 1.0 mm thick and 20 mm wide. There is a 10-A current through this cross section, with the charge carriers traveling down the length of the strip. The strip is placed in a uniform magnetic field that has a magnitude of 2.0 T and is directed perpendicular to both the length and the width of the strip. If the number density of free electrons in copper is $8.47 \times 10 ^ { 19 } \mathrm { mm } ^ { - 3 }$, calculate (a) the speed of the electrons in the strip and (b) the potential difference across the strip width.

(a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a $0.500 - \mu C$ charge and flies due west at a speed of 660. m/s over Earth’s south magnetic pole, where the $8.00 \times 10 ^ { - 5 } - \mathrm { T }$ magnetic field points straight up. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.

Rectangular bars of copper and aluminum are held by pins at their ends, as shown in the figure. Thin spacers provide a separation between the bars. The copper bars have cross-sectional dimensions 0.5 in. x 2.0 in., and the aluminum bar has dimensions 1.0 in. x 2.0 in. Determine the shear stress in the 7/16-in. diameter pins if the temperature is raised by 100$^{\circ}$F. (For copper, E$_c$ = 18,000 ksi and $\alpha_c$ = 9.5 x 10$^{-6}$/$^{\circ}$F; for aluminum, E$_a$ = 10,000 ksi and $\alpha_a$ = 13 X 10$^{-6}$/$^{\circ}$F.)

Rectangular bars of copper and aluminum are held by pins at their ends. Thin spacers provide a separation between the bars. The copper bars have cross-sectional dimensions 0.5 in. $\times 2.0$ in., and the aluminum bar has dimensions 1.0 in. $\times 2.0 in$.

Determine the shear stress in the 7 / 16 in. diameter pins if the temperature is raised by $100^{\circ} F$.