U3AOS2 Topic 5: Electrical Forces


Electric forces are a fundamental aspect of electromagnetism, which is one of the four fundamental forces of nature. 

These forces arise due to the presence of electric charges and can either attract or repel charged objects. 

Understanding electric forces is crucial for comprehending various phenomena in physics, from the behavior of subatomic particles to the workings of everyday electronic devices.

Basics of Electric Charges

Electric charge is a property of subatomic particles, such as electrons and protons, that causes them to experience a force when placed in an electric field. 

There are two types of charges: 

                        positive and negative. 

Protons carry a positive charge, while electrons carry a negative charge. Like charges repel each other, and unlike charges attract each other.


The SI unit of electric charge is the Coulomb (C).

 A single proton has a charge of +1.6 x 10^-19 C, while a single electron has a charge of -1.6 x 10^-19 C.

Coulomb's Law

Coulomb's Law quantifies the electric force between two charged objects. It states that the electric force F between two point charges q1​ and q2​ is directly proportional to the product of the charges and inversely proportional to the square of the distance rrr between them:

F=ke(q1q2) / r2

where ke is Coulomb's constant, approximately equal to 8.99×109 N m2/C2. This law shows that the force decreases rapidly as the distance between the charges increases.

Electric Field

An electric field is a region around a charged object where other charges experience a force. The electric field E at a point in space is defined as the electric force F per unit charge q:

                                                    E=F/q

The direction of the electric field is the direction of the force experienced by a positive test charge placed in the field. Electric field lines represent the field's strength and direction, emanating from positive charges and terminating on negative charges.

Superposition Principle

The principle of superposition states that the total electric force on a charge due to multiple other charges is the vector sum of the individual forces exerted by each charge. If a charge q is influenced by charges q1,q2,…,qn the total force  F total​ is given by:

F total= F1+F2+…+Fn 

where F1,F2,…,Fn​ are the forces exerted by q1,q2,…,qn respectively.

Electric Potential Energy

Electric potential energy is the energy a charged object possesses due to its position in an electric field. For a system of two point charges q1​ and q2​, separated by a distance r, the electric potential energy U is:

U= ke(q1q2) / r

This energy is positive if the charges are of the same sign (repulsive force) and negative if the charges are of opposite signs (attractive force).

Applications of Electric Forces

Electric forces play a crucial role in numerous applications and natural phenomena:

  1. Atomic Structure: Electrons are held in orbit around the nucleus of an atom due to the electric force between the negatively charged electrons and the positively charged protons in the nucleus.

  2. Electronics: Electric forces are the basis for the operation of electronic components such as capacitors, resistors, and transistors. These components control the flow of electric charges in circuits.

  3. Electrostatic Precipitators: These devices use electric forces to remove dust and other particles from the air by charging the particles and attracting them to oppositely charged plates.

  4. Van de Graaff Generators: These machines generate high voltages by accumulating electric charges on a metal dome, demonstrating electric forces' ability to create strong fields and potential differences.

  5. Lightning: Electric forces cause the buildup of charges in clouds, leading to the discharge of electricity in the form of lightning during thunderstorms.

Conclusion

Electric forces are a key concept in understanding the interactions between charged particles. They are described by Coulomb's Law, the superposition principle, and are visualized using electric fields. These forces have numerous applications in technology and nature, making them an essential topic in the study of physics.


Point Charge: is an electron or a positron

Two Point Charges: is an electron and electron, electron and positron or a positron and a positron


When a particle or multiple particles are in fields they will have forces being applied to them due to repelling or attracting. These forces are calculated with the following formulas.


Force on a point charge


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Force on two point charges


�=��1∗�2�2

The following simulation shows the force being applied to a particle in a uniform electric field.

Created with GeoGebra®, by Tom Walsh, Link

Example 1
Calculate the electric force between two point charges of 2 μC2 \, \mu C and 3 μC3 \, \mu C separated by a distance of 0.05 m0.05 \, m.

 Use Coulomb's Law: F=kq1q2r2F = k \frac{q_1 q_2}{r^2} F=(8.99×109 Nm2/C2)(2×10−6 C)(3×10−6 C)(0.05 m)2F = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \frac{(2 \times 10^{-6} \, \text{C})(3 \times 10^{-6} \, \text{C})}{(0.05 \, \text{m})^2}

F=21.57 NF = 21.57 \, N


Example 2
 If the distance between two charges is doubled, what happens to the force?

According to Coulomb's Law, if rr is doubled, FF is reduced by a factor of 44 [1].

F′=F4F' = \frac{F}{4}

Example 3
 Calculate the net force on a charge q2q_2 placed between q1q_1 and q3q_3 where q1=1 μCq_1 = 1 \, \mu C, q2=−2 μCq_2 = -2 \, \mu C, q3=3 μCq_3 = 3 \, \mu C, and distances r12=0.1 mr_{12} = 0.1 \, m, r23=0.2 mr_{23} = 0.2 \, m.

Calculate individual forces and use superposition principle. F12=kq1q2r122F_{12} = k \frac{q_1 q_2}{r_{12}^2}

F23​=kr232​q2​q3​​

​

 Fnet=F12+F23F_{net} = F_{12} + F_{23}

Example 4
Compare the electric force to gravitational force between two electrons.

Use Fe=ke2r2F_e = k \frac{e^2}{r^2} and

Fg=Gme2r2F_g = G \frac{m_e^2}{r^2}


FeFg=ke2Gme2\frac{F_e}{F_g} = \frac{k e^2}{G m_e^2}

FeFg≈1042\frac{F_e}{F_g} \approx 10^{42} [4]

Example 5
Find the electric field at a point due to a point charge of 5 μC5 \, \mu C at a distance of 0.1 m0.1 \, m.

Use  E=kqr2E = k \frac{q}{r^2} E=(8.99×109 Nm2/C2)5×10−6 C(0.1 m)2E = (8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2) \frac{5 \times 10^{-6} \, \text{C}}{(0.1 \, \text{m})^2}

E=4.495×106 N/CE = 4.495 \times 10^6 \, \text{N/C}


Example 6
A charge of 2 μC2 \, \mu C is placed in a uniform electric field of 105 N/C10^5 \, \text{N/C}. Find the force on the charge.

 Use F=qEF = qE

F=(2×10−6 C)(105 N/C)F = (2 \times 10^{-6} \, \text{C})(10^5 \, \text{N/C})

F=0.2 NF = 0.2 \, N

Exercise &&1&& (&&1&& Question)

Calculate the electric potential energy of two charges 1 μC1 \, \mu C and 2 μC2 \, \mu C separated by 0.1 m0.1 \, m.

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Exercise &&2&& (&&1&& Question)

Find the potential difference between two points separated by 0.5 m0.5 \, m in a field of 100 N/C100 \, \text{N/C}.

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Exercise &&3&& (&&1&& Question)

Two identical conducting spheres, each with a charge of 1 μC1 \, \mu C, are 0.3 m0.3 \, m apart. Calculate the force.

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Exercise &&4&& (&&1&& Question)

Three 1 μC1 \, \mu C charges form an equilateral triangle of side 0.2 m0.2 \, m. Calculate the force on one charge.

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Exercise &&5&& (&&1&& Question)

Find the acceleration of an electron in an electric field of 500 N/C500 \, \text{N/C}.

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Exercise &&6&& (&&1&& Question)

 Calculate the work done in moving a 2 μC2 \, \mu C charge across 0.5 m0.5 \, m in an electric field of 200 N/C200 \, \text{N/C}.

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Exercise &&7&& (&&1&& Question)

Calculate the torque on an electric dipole in a uniform electric field of 100 N/C100 \, \text{N/C} with a dipole moment of 10−9 Cm10^{-9} \, \text{Cm}.

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