# Fields

## Fields Revision

**Fields and Gravitational Field Strength**

GCSE Physics introduced the idea of **forces** and **force fields**. In this section we begin looking at the different types of **field** you will encounter.

**Fields**

A **force field** (such as a magnetic field or electric field) is the area in which a body will experience a **force**. The force will be a **non-contact force** as no contact is needed between the field and the body. Below are some examples of some **contact** and **non-contact **forces:

**Contact Forces**:

- Push and pull
- Tension
- Friction
- Air resistance
- Water resistance
- Normal contact force

**Non-contact Forces**:

- Electrostatic forces
- Magnetic force
- Gravitational force (Weight)

Only **non-contact forces** can have **force fields**.

**Drawing Force Fields**

As with any **force**, when drawing **force fields**, it is important to show the** magnitude** and** direction** of the force as forces are **vector** quantities. Some important things to remember when drawing field lines are:

- Circular or spherical objects like the Earth can be considered as a
**point mass/charge**. - A
**uniform force field**is one in which the field is**equal**at all points within the field. - The closer the field lines, the
**stronger**the field.

On the right, we can see a representation of the **gravitational field** around the Earth.

We can see that the **field lines **are **non-uniform** as the distance between the field lines varies with distance from the centre.

On the diagram on the right, the Earth is represented as a **point mass**.

Any spherical object which has its mass evenly spread like a star or a planet may be considered a **point mass**.

**Gravitational Field Strength**

Any object with a **mass** exerts a force of attraction in the area around it known as **gravity**. The greater the **mass **of the object, the greater the **field strength** produced. For most common objects we do not feel the effects of this force as their **mass **and **field strength** is tiny compared to that of the Earth.

**Gravitational forces** always act towards the centre of the object and can only be an **attractive force**.

The **gravitational field strength **at any point within a **gravitational field **is defined as the** force per unit of mass **exerted on a body. We need to recall that the **gravitational field strength** \left(g\right) on Earth is approximately 9.81 \: \text{Nkg}^{-1}, but this number varies for other planets and stars. This can be represented in the equation:

g = \dfrac{F}{m}

- g is the
**gravitational field strength**in Newtons per kilogram \left(\text{Nkg}^{-1}\right). - F is the
**force**in Newtons \left(\text{N}\right). - m is the
**mass**in kilograms \left(\text{kg}\right).

**Example: **Calculate the force exerted on a 70 \: \text{kg} object on a planet with \dfrac{1}{3} of the gravitational field strength of Earth.

**[2 marks]**

We know that g on earth is 9.81 \: \text{Nkg}^{-1}, then g on the planet will be \dfrac{9.81}{3} = \boldsymbol{3.27 \: }\textbf{Nkg}^{-1}.

g = \dfrac{F}{m} rearranges to F = g \times m.

F = 3.27 \times 70 = \boldsymbol{230} \: \textbf{N}.

**Mass and Weight**

The **mass** of an object is determined by the amount of **matter** that makes the object up and is measured in kg. This does not change even if **gravitational field strength** does. Therefore it can be considered a constant.

However, **weight** is a** force** \left(N\right) and it is determined by** gravitational field strength**. Therefore, we can write the following equation based on our **gravitational field strength** equation:

W = m \times g

- W is
**weight**in Newtons \left(N\right). - m is
**mass**in \left(\text{kg}\right). - g is
**gravitational field strength**in Newtons per kilogram \left(\text{Nkg}^{-1}\right).

**Weight** is not constant on different planets/stars. This is because **weight **is dependent upon the **gravitational field strength** of the planet/star that the object is on.

**Drawing Gravitational Fields**

**Gravitational fields** are an example of a **radial field**.

Radial fields act towards the centre of the mass and are an attractive force. They act **radially** inwards towards the point mass.

For massive objects like planets or stars, we can represent the object as a** point mass**.

However, if we were to look at a smaller part of the surface of a planet, the curvature is so small that the surface could be considered flat.

Therefore the** gravitational field strength** could be represented as a **uniform field**.

## Fields Example Questions

**Question 1:** What is a force field?

**[1 mark]**

**The area around a body that will experience a non contact force.**

**Question 2:** Below is a field around a point mass. How would you expect this field to be different for another point mass with a stronger field?

**[1 mark]**

**The field lines would be closer together at all points around the point mass.**

**Question 3:** Define gravitational field strength.

**[1 mark]**

The **force per unit of mass** exerted on a body. It may also be defined as an equation where \boldsymbol{g= \dfrac{F}{m}}.

**Question 4:** The diagram below shows a uniform gravitational field. How would the diagram change if a change in density caused the field strength to be non-uniform?

**[2 marks]**

The **field lines would no longer be equal distances apart.** Areas where the field strength was **stronger would have field lines that are closer together and where the field strength is weaker the lines would be further apart**.

**Question 5:** Calculate the mass of a body of weight 800 \: \text{N} on a planet of gravitational field strength of 15 \: \text{Nkg}^{-1}.

**[2 marks]**