(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 maximum torque on a 150-turn square loop of wire 18.0 cm on a side that carries a 50.0-A current in a 1.60-T field? (b) What is the torque when $\theta$ is $10.9 ^ { \circ }$?

$(a)$ 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 long solenoid with n = 10 turns per centimeter has a cross-sectional area of $5.0 \mathrm { cm } ^ { 2 }$ and carries a current of 0.25 A. A coil with five turns encircles the solenoid. When the current through the solenoid is turned off, it decreases to zero in 0.050 s. What is the average emf induced in the coil?

$(a)$ 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) 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 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 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 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) 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.

Calculate the reactance of a $5.0 - \mu \mathrm { F }$ capacitor at (a) 60 Hz, (b) 600 Hz, and (c) 6000 Hz.

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.

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?

For each equation, tell whether its graph is a horizontal or a vertical line. y = -0.25.