Electric Charges and Fields

M. Rocha

Physics 4B - Chapter 5 (OpenStax)

Electrostatics

Electricity at rest

Electrical Forces

There are two types of electrical charge:

Positive and Negative

Like charges repel, opposite charges attract

Origin of Charge

Charge comes from Electrons and Protons

Proton charge = e

Electron charge = -e

e is called the elementary charge

Chekpoint

What is the total charge of an object with 6 electrons and 5 protons?

Total charge = -6 e + 5 e = -1 e

Charge is quantized

The elementary charge e is the smallest unit of charge

No smaller units of charge have ever been observed, all charged objects have a charge that is a whole-number multiple of e, the smallest quantum of charge

quarks have never been observed alone, they are always in a combination so that their charge sums to e, -e or zero

Charging by Friction/Contact

Electrons move easily, so an object can become charged by rubbing electrons off an object’s surface

Chekpoint

When you rub a balloon against your hair the balloon gets electrically charged, this is because

Electrons are released from the fur and stick on the balloon

Human Electroscope

Van der Graaf Demo Video

Conservation of Charge

Charge cannot be created nor destroyed.

Objects become charged by transfer of charges

Conductors and Insulators

Conductors: Materials in which electrons flow freely, such as metals

Insulators: Materials in which electrons do not move easily, such as plastic and wood

Semiconductors: Materials that can act as conductors or insulators under different conditions, such as silicon

Lightning

Air is an insulator but at high voltages it can conduct electricity as lightning

Music Tesla Coil

Lightning

Air is an insulator but at high voltages it can conduct electricity as lightning

Charging by Induction

If a charged object is brought near a conducting surface, even without physical contact, electrons will move in the conducting surface

Charging by Induction

If a charged object is brought near a conducting surface, even without physical contact, electrons will move in the conducting surface

Charge Polarization

Charge polarization occurs when the positions of the electrons and protons in an atom are skewed

Charge Polarization

Charge polarization occurs when the positions of the electrons and protons in an atom are skewed

Coulomb's Law

Electric force acts at a distance just like Gravity

And also like Gravity the magnitude of the Electric Force is proportional to the product of charge and inversely proportional to the square of the distance

Coulomb's Law

Electric force acts at a distance just like Gravity

And also like Gravity the magnitude of the Electric Force is proportional to the product of charge and inversely proportional to the square of the distance

F_\mathrm{Electric} = k \frac{q_1 q_2}{d^2}

Coulomb's Law

\vec{F}_\mathrm{Electric} = k_e \frac{q_1 q_2}{r^2}\hat{r}

The SI unit of charge is the coulomb (C)

A charge of 1 C is the charge of 6.24 × 10^18 e

e = 1.6 × 10^-19 C

Coulomb's Law

The SI unit of charge is the coulomb (C)

A charge of 1 C is the charge of 6.24 × 10^18 e

e = 1.6 × 10^-19 C

\vec{F}_\mathrm{Electric} = k_e \frac{q_1 q_2}{r^2}\hat{r}

Chekpoint

A charge Q is placed at the point P shown below. What is the force on Q?

Q = 2 \mu C

\vec{F}_\mathrm{Electric} = k_e \frac{q_1 q_2}{r^2}\hat{r}

\vec{F}_{1} \ =\ \frac{k\ Q\ q_{1}}{r^{2}}\hat{r} \ =\ 9\times 10^{9} \ \frac{Nm^{2}}{C^{2}}\frac{\left( 2\times 10^{-6} \ C\right)\left( 1\times 10^{-6} \ C\right)}{( 3\ m)^{2}}\hat{r} \ =2\times 10^{-3} \ N\ \ \hat{i}\\

\vec{F}_{2} \ =\ \frac{k\ Q\ q_{2}}{r^{2}}\hat{r} \ =\ 9\times 10^{9} \ \frac{Nm^{2}}{C^{2}}\frac{\left( 2\times 10^{-6} \ C\right)\left( -3\times 10^{-6} \ C\right)}{( 1\ m)^{2}} \ \hat{r} = -54\times 10^{-3} \ N\ \hat{i}\\

\vec{F} =\vec{F}_{1} +\vec{F}_{2} =( 2 -54) \times 10^{-3} \ N\ \hat{i} \ =\ -0.052\ N\ \hat{i}

The eight source charges each apply a force on the single test charge Q. Each force can be calculated independently of the other seven forces. This is the essence of the superposition principle.

The net electric force on a test charge Q is the vector sum of all the electric forces acting on it

Electric Field

Each of these eight source charges creates its own electric field at every point in space; shown here are the field vectors at an arbitrary point P. Like the electric force, the net electric field obeys the superposition principle.

\Rightarrow E(P) = E(x,y,z)

Electric Field

The direction of the E field is radially away from the source charge. A positive test charge placed in this field would accelerate radially away from the nucleus (since it is also positively charged). The convention is that the direction of the electric field vector is defined in terms of the direction of the force it would apply to positive test charges.

Electric Field Lines

Electric field lines indicate the direction of electric force if a positive charge was placed in the electric field

Continuous Charge Distributions

The configuration of charge differential elements for a (a) line charge, (b) sheet of charge, and (c) a volume of charge. Also note that (d) some of the components of the total electric field cancel out, with the remainder resulting in a net electric field.