(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) 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 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 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.

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?

Determine the number of different triangles that can be formed using the given measurements. Then solve the triangles. Round to the nearest tenth.

$$m \angle C = 45 ^ { \circ } , b = 10 , c = 5$$

(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 $2.2 - \mathrm { k } \Omega$ resistor is connected across a D cell battery (1.5 V). What is the current through the resistor?

Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows.

What is the maximum voltage that can be applied across a $2.7-\mathrm{k} \Omega$ resistor rated at $\frac{1}{4}$ watt?

How many volts are supplied to operate an indicator light on a DVD player that has a resistance of 140 $\Omega$ , given that 25.0 mA passes through it?

What current flows through the bulb of a 3.00-V flashlight when its hot resistance is $3.60 \Omega$?

The current supplied to an air conditioner unit is 4.00 amps. The air conditioner is wired using a 10-gauge (diameter 2.588 mm) wire. The charge density is n = 8.48 $\times$ 10$^{28}$ electrons/m$^3$ . Find the magnitude of (a) current density and (b) the drift velocity.