(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) 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 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?

What Hall voltage is produced by a 0.200-T field applied across a 2.60-cm-diameter aorta when blood velocity is 60.0 cm/s?

$(a)$ At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? $(b)$ What would the radius of the path be if the proton had the same speed as the electron? $(c)$ What would the radius be if the proton had the same kinetic energy as the electron? $(d)$ The same momentum?

A copper wire of cross-sectional area $1.00 \mathrm { mm } ^ { 2 }$ has a current of 2.0 A flowing along its length. What is the drift speed of the conduction electrons? Assume 1.3 conduction electrons per copper atom. The mass density of copper is 9.0 $\mathrm { g } / \mathrm { cm } ^ { 3 }$ and its atomic mass is 64 g/mol.

(a) An oxygen-16 ion with a mass of $2.66 \times 10^{-26} \mathrm{kg}$ travels at $5.00 \times 10^{6} \mathrm{m} / \mathrm{s}$ 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 $7.50 \times 10^{6} \mathrm{m} / \mathrm{s}$ 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?

A cosmic ray proton travels in a circle with a radius of $95 \mathrm{~m}$ perpendicular to Earth's magnetic field. If the proton's speed is $10^6 \mathrm{~m} / \mathrm{s}$, then what is the field strength at the proton's location?

(a) Given a 48.0-V battery and $24.0-\Omega$ and $96.0-\Omega$ resistors, find the current and power for each when connected in series. (b) Repeat when the resistances are in parallel.

A flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp?

An electron in a TV CRT moves with a speed of $6.0 \times 10^7 \mathrm{~m} / \mathrm{s}$, in a direction perpendicular to Earth's field, which has a strength of $5.0 \times 10^{-5} \mathrm{~T}$. $(a)$ What strength electric field must be applied perpendicular to the Earth's field to make the electron moves in a straight line? (b) If this is done between plates separated by $1.00 \mathrm{~cm}$, what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a correction.)

(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) 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?