$(a)$ What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? $(b)$ Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.

Calculate the magnitude and direction of the electric field 2.0 m from a long wire that is charged uniformly at $\lambda = 4.0 \times 10 ^ { - 6 } \mathrm { C } / \mathrm { m }$.

Suppose a speck of dust in an electrostatic precipitator has $1.0000 \times 10^{12}$ protons in it and has a net charge of -5.00 nC (a very large charge for a small speck). How many electrons does it have?

To start a car engine, the car battery moves $3.75 \times 10^{21}$ electrons through the starter motor. How many coulombs of charge were moved?

An amoeba has $1.00 \times 10^{16}$ protons and a net charge of $0.300 \mathrm{pC}$. How many fewer electrons are there than protons?

Common static electricity involves charges ranging from nanocoulombs to microcoulombs. How many electrons are needed to form a charge of -2.00 nC?

Common static electricity involves charges ranging from nanocoulombs to microcoulombs. How many electrons must be removed from a neutral object to leave a net charge of $0.500 \mu \mathrm{C}$ ?

Two point particles with charges $+ 3 \ \mu\text{C}$ and $+5 \ \mu\text{C}$ are held in place by 3-N forces on each charge in appropriate directions. (a) Draw a free-body diagram for each particle. (b) Find the distance between the charges.

A 4.00-pF is connected in series with an 8.00-pF capacitor and a 400-V potential difference is applied across he pair. (a) What is the charge on each capacitor? (b) What is the voltage across each capacitor?

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

What is the maximum voltage that can be applied to a 10-k $\Omega$ resistor rated at 14W ?

Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has $\alpha$ = −0.06/$^o$C ) when it is at the same temperature as the patient. What is a patient’s temperature if the thermistor’s resistance at that temperature is 82.0% of its value at 37 $^o$C (normal body temperature)?

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 $3.60 \Omega$?