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) 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) 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 strip of copper is placed in a uniform magnetic field of magnitude $2.5 \mathrm{~T}$. 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 $1 / \mathrm{nq}$ ?

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?

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?

$(a)$ 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?

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 $100^{\circ} F$.

(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 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 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?

Solve each problem using Polya’s four-step problem-solving strategy. Label your work so that each of Polya’s four steps is identified. An investor bought 20 shares of stock for a total cost of $1200 and then sold all the shares for$1400. A few months later, the investor bought 25 shares of the same stock for a total cost of $1800 and then sold all the shares for$1900. How much money did the investor earn on these investments

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.

(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.