(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.

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) An oxygen-16 ion with a mass of $2.66 \times 10 ^ { - 26 } \mathrm { kg }$ travels at $5.0 \times 10 ^ { 6 } \mathrm { m } / \mathrm { s }$ perpendicular to a 1.20-T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an electron? (c) Discuss why the ratio found in (b) should be an integer.

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?

$(a)$ By how many percent is the torque of a motor decreased if its permanent magnets lose $5.0 \%$ of their strength? $(b)$ How many percent would the current need to be increased to return the torque to original values?

(a) A DC power line for a light-rail system carries 1000 A at an angle of $30.0^{\circ}$ to the Earth’s $5.00 \times 10^{-5}-\mathrm{T}$ field. What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.

A 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) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?

(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.

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 $100^{\circ} F$.

Calculate the magnetic force on a hypothetical particle of charge $1.0 \times 10 ^ { - 19 } \mathrm { C }$ moving with a velocity of $6.0 \times 10 ^ { 4 } \hat { \mathbf { i } } \mathrm { m } / \mathrm { s }$ in a magnetic field of $1.2 \hat { \mathbf { k } } \mathrm { T }$.

A strip of copper is placed in a uniform magnetic field of magnitude 2.5 T. The Hall electric field is measured to be $1.5 \times 10 ^ { - 3 } \mathrm { V } / \mathrm { m }$. (a) What is the drift speed of the conduction electrons? (b) Assuming that $\mathrm { n } = 8.0 \times 10 ^ { 28 }$ electrons per cubic meter and that the cross-sectional area of the strip is $5.0 \times 10 ^ { - 6 } \mathrm { m } ^ { 2 }$, calculate the current in the strip. (c) What is the Hall coefficient 1/nq?

(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?

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 T. Determine (a) the rotational period of the circulating protons and (b) the maximum radius of the protons’ orbit.