$(a)$ 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 $1.20 \mathrm{~T}$ magnetic field, which makes it move in a circular arc with a $0.231 \mathrm{~m}$ 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) What voltage will accelerate electrons to a speed of $6.00 \times 10 ^ { - 7 } \mathrm { m } / \mathrm { s }$? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with the radius of curvature of an electron accelerated through the same potential.

(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) 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) What is the force per meter on a lightning bolt at the equator that carries 20,000 A perpendicular to Earth’s $3.0 \times 10 ^ { - 5 } \mathrm { T }$ field? (b) What is the direction of the force if the current is straight up and Earth’s field direction is due north, parallel to the ground?

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 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 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?

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 wire carrying a 30.0-A current passes between the poles of a strong magnet that is perpendicular to its field and experiences a 2.16-N force on the 4.00 cm of wire in the field. What is the average field strength?

(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 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 150-W lightbulb emits 5% of its energy as electromagnetic radiation. What is the radiation pressure on an absorbing sphere of radius 10 m that surrounds the bulb?

A plane electromagnetic wave travels northward. At one instant, its electric field has a magnitude of 6.0 V/m and points eastward. What are the magnitude and direction of the magnetic field at this instant?