Description and Property of Fields – SS1 Physics Lesson Note (Third Term)

A field is a region or space under the influence of some physical agency such as gravity, electricity or magnetism.

Behavioural objectives

By the end of the lesson, students should be able to:

1. define a field and name the three types of field;
2. state Newton’s law of universal gravitation and define acceleration due to gravity;
3. describe a magnetic field and its lines of force;
4. state the properties of electric lines of force;
5. state Coulomb’s law;
6. define electric field intensity, electric field potential and flux density.

What are the types of field?

There are three main types of field: gravitational, magnetic and electric fields.

What is a gravitational field?

A gravitational field is any region or space around a mass in which the gravitational force of the mass is felt.

• Upward throw: a massive object thrown up rises to its highest point.
• Brief pause: the object stays stationary very briefly at the top.
• Downward fall: the object falls faster and faster until it hits the ground.
• Cause: the up and down movements of objects on the earth’s surface are due to the gravitational field.
• Direction of force: gravitational force is always a force of attraction.

What is the force of gravity?

The force of gravity is the pull of attraction between the earth and objects on or near it.

• Weight: the force of gravity on an object is its weight, given by W = mg.

What is Newton’s law of universal gravitation?

Newton’s law of gravitation states that the force of attraction between two bodies of masses M₁ and M₂ is directly proportional to the product of their masses and inversely proportional to the square of the distance R between their centres.

Mathematical expression

• F ∝ M₁M₂ / R²
• F = GM₁M₂ / R²

Meaning of the symbols

• F: the gravitational force on either particle, in newtons (N).
• M₁ and M₂: the masses of the two bodies, in kilograms (kg).
• R: the distance between the centres of the bodies, in metres (m).
• G: the universal gravitational constant. Its numerical value depends on the units used for force, mass and length.
• G in SI units: about 6.67 × 10⁻¹¹ N m² kg⁻².

What is acceleration due to gravity?

Acceleration due to gravity is the acceleration of objects caused by the earth’s gravitational attraction.

• Symbol: g.
• Average value: about 9.81 m s⁻².
• Free fall: without air resistance, objects of different masses released from rest at the same point reach the ground at the same time.

What is the difference between g and G?

The symbol g is the acceleration due to gravity, and G is the universal gravitational constant.

What is a magnetic field?

A magnetic field is the region or space around a magnet in which the influence of the magnet can be felt or detected.

How do we show the magnetic lines of force of a magnet?

The pattern of magnetic lines of force can be shown with iron filings or a compass needle.

Iron filings method

1. Place a white sheet of paper over the magnet.
2. Sprinkle iron filings on the paper.
3. Tap the paper gently.
4. The filings arrange themselves in a definite pattern, which shows the lines of force.

Compass needle method

1. Place the magnet on a sheet of paper.
2. Place a small compass near one pole and mark the positions of the ends of the needle.
3. Move the compass so that one end of the needle lies on the last mark, then mark the new position.
4. Repeat until you reach the other pole, then join the marks with a smooth line.

What is a line of force?

A line of force is an imaginary line drawn so that its direction at any point (the direction of the tangent) is the same as the direction of the field at that point.

• Direction: outside a magnet, magnetic lines of force run from the north pole to the south pole.
• Crossing: two lines of force never cross each other.
• Spacing: the lines are closer together where the field is stronger, as near the poles.

What is an electric field?

An electric field is any region where a charge experiences a force of electrical origin.

• Positive charge: one of the two types of charge.
• Negative charge: the other type of charge.
• Like charges: they repel each other.
• Unlike charges: they attract each other.

What are electric lines of force?

An electrostatic line of force is a line whose tangent is in the direction of the force on a small positive charge at that point.

• Mapping: electric fields can be mapped out by electrostatic lines of force.
• Arrows: arrows on the lines show the direction of the force on a positive charge.
• Negative charge: the force on a negative charge is in the opposite direction.
• Shape: the direction of a field varies from point to point, so lines of force are usually curves.

1. Isolated positive charge: lines point outwards from the charge.
2. Isolated negative charge: lines point inwards towards the charge.
3. Unlike charges (positive and negative): lines curve from the positive charge to the negative charge.
4. Like charges (positive and positive): lines push away from each other and do not join the two charges.

What are the properties of lines of force?

1. Lines of force never intersect.
2. Lines of force are usually curves, as the direction of a field varies from point to point.
3. In a uniform field, the lines of force are straight, parallel and uniformly spaced.
4. No lines of force originate or terminate in the space surrounding a charge.
5. Every line of force in an electrostatic field is a continuous line terminated by a positive charge at one end and a negative charge at the other end.

What is Coulomb’s law?

Coulomb’s law states that the force between two charges Q₁ and Q₂ separated by a distance r is directly proportional to the product of the charges and inversely proportional to the square of their distance apart.

• Other name: the inverse square law.
• F ∝ Q₁Q₂
• F ∝ 1/r²
• F ∝ Q₁Q₂ / r²

Mathematical expression

• F = K Q₁Q₂ / r² ______ (i)
• K: the constant of proportionality, K = 9 × 10⁹ N m² C⁻².
• K in terms of ε₀: K = 1/(4πε₀).
• ε₀: the permittivity of free space (vacuum), measured in farad per metre (F/m).
• Q: charge, in coulombs (C).
• r: distance between the charges, in metres (m).

What is electric field intensity?

Electric field intensity (E) is the force per unit charge.

• Formula: E = F/Q ______ (ii)
• Type of quantity: vector.
• Unit: newton per coulomb (N C⁻¹).

What is electric field potential?

Electric field potential (V) is the work done in moving a unit positive charge from infinity to a point in the field.

• Other definition: work done per unit charge.
• Formula: V = W/Q.
• Type of quantity: scalar.
• Unit: joule per coulomb (J C⁻¹), also called the volt (V).

What is flux density?

Flux density (D) is the charge per unit area.

• Formula: D = Q/A.
• Unit: coulomb per square metre (C m⁻²).

What are the electric field quantities at a glance?

The table below compares the three electric field quantities.

Evaluation

1. Define a field and name the three types of field.
2. State Newton’s law of universal gravitation.
3. State three properties of lines of force.
4. State Coulomb’s law and write its mathematical expression.
5. Define electric field intensity and state its formula.

Assignment

Define electric field potential and flux density. Give the formula and unit of each.