# Magnitude in Physics

Magnitude in physics refers to the maximum extent of size and the direction of an object. It is used in both vector and scalar quantities as a common factor. For example, a scalar quantity has magnitude only, it does not have or require direction for describing itself.

Magnitude allows us to compare the speed of different moving objects, the distance covered by a moving object and also tells the amount of an object.

For example, in the case of a moving car which is moving faster than a motorcycle, the magnitude of the speed of the car is more than the magnitude of the speed of the motorcycle. In physics, there are two types of quantity: scalar and vector.

A scalar quantity such as speed has only magnitude, not direction. Whereas, a vector quantity has both magnitude and direction such as velocity. Here are some ways in which magnitude is used:

• Magnitude of earthquake
• Magnitude of electron's charge
• Magnitude of gravitational force
• Magnitude of force, displacement, etc.

### 1. Magnitude of Earthquake:

An earthquake's magnitude is defined in terms of length, breadth and width. We can say that it refers to the physical size of an earthquake. It causes different shaking in different places that is due to the type of surface material and the distance from the epicentre. Its magnitude is denoted by whole numbers including decimal fractions. An earthquake of magnitude 5.3 is considered a moderate earthquake and considered strong if the magnitude is 6 or more.

When an earthquake occurs, a large amount of energy is released that causes seismic waves, which travel in all directions and shake the earth and cause destruction. The magnitude of an earthquake helps predict the chances of its occurrence in future. The scale that measures an earthquake's magnitude is called the Richter scale. In this scale, with each increase in number the magnitude increases ten times.

### 2. Magnitude of Charge on an Electron

The charge on an electron is equal to the magnitude of the elementary charge, e with a negative sign. For example, 1.602 x 10-19. Further, there are two types of electrical charges: positive and negative. Protons carry a positive charge and electrons carry a negative charge. The net charge of an atom is said to be positive if it has more protons than electrons. Similarly, if an atom has a negative charge if electrons are more than protons. When it has an equal number of electrons and protons, it is said to be electrically neutral.

### 3. Magnitude of Force

It refers to the sum of all the forces that act on an object. If all the forces act in the same direction, it increases the magnitude of force. If these forces act in different directions, the magnitude of the force decreases as the forces acting in opposite directions will cancel out or neutralize the effect of each other.

### 4. Magnitude of Displacement

Displacement refers to the shortest possible distance between the initial and final position of the object. The magnitude of displacement for a moving object is always either less or equal to the distance travelled. For example, if an object moves in a straight line and covers a distance of 5 meters then its distance and displacement will be the same.

### 5. Magnitude of Gravitational Force

It refers to the force that attracts any two objects with mass. It is an attractive force as it tends to pull masses together. We can say there is an attraction or every object is attracting or pulling every other object in this universe. It is also known as Newton's Universal law of Gravitation. The magnitude of this gravitational force between two objects with mass m1 and m2 is represented mathematically as shown below;

F = G x m1 x m2/r2

## How to calculate the magnitude of a physical quantity?

Every physical quantity has magnitude, so it is measurable. But, all physical quantities cannot be measured in a similar way. This is because a physical quantity can be of two types: scalar and vector. Both types follow different rules of the algebra.

### Scalar Quantity:

It is a physical quantity which is specified by only magnitude or it has only magnitude such as mass, volume, density, etc. So, only magnitude and unit are needed to define a scalar quantity, direction is not needed. For example, 60 Kg weight, wherein 60 is the magnitude and Kg is the unit. To calculate the magnitude of a scalar quantity linear algebra rule is required to follow.

Likewise, speed is also a scalar quantity as it is described only by its magnitude. It just tells the rate at which an object is moving, don't tell anything about the direction in which it is moving. So, an object that is moving faster will cover more distance than an object that is moving slower in the same amount of time.

How to calculate the magnitude of a scalar quantity:

Its calculation is very simple. In our daily life, we calculate scalar quantity lots of times. For example, you cover a distance of 10km to reach your office, in this case, a distance of 10 km is a scalar quantity and its magnitude is 10 km which is equal to the total distance covered.

In another example, suppose 100 ml of water is mixed with 1 litre of pure milk and the total quantity or magnitude of milk becomes 1250 ml. Here, magnitude is calculated by using simple addition.

### Vector Quantity

It is a physical quantity that has both magnitude and direction such as velocity, displacement, force, etc. we can say that it needs both magnitude and direction for its complete description. So, to define a vector, both magnitude and direction are required. For example, a velocity of 60 km/hr, north. Here, an object is moving at a speed of 60 km/hr (magnitude) towards the north.

The addition of two vector quantities cannot be done by using ordinary algebra. A vector quantity is denoted by an arrow over a letter or a line segment with an arrow at one end wherein the arrow tells the direction.

How to calculate the magnitude of a vector quantity:

In the case of vector quantities, two or more vectors can be called equal if they have the same direction and magnitude. When we multiply a vector quantity with a positive integer, its magnitude changes, but its direction remains the same. However, when we multiply it with a negative integer, both magnitude and direction change as direction is reversed and magnitude is multiplied by the absolute value of the number.

## Order of Magnitude

Order of magnitude is a rough estimate of the size or magnitude of something and is represented as a power of ten. It is the estimated size of something measured in the powers of 10. For example, the size of the Earth is of the order of magnitude of 1020 kg.

If a value is an order of magnitude larger than another value, it means, it is ten times larger than another value. Likewise, when it is two orders of magnitude larger, it would be a hundred times larger. The order of magnitude can be seen in scientific notations where a number is raised to the power of 10.

### How to find the order of magnitude?

The order of magnitude of 255000 would be 5 as when this value is converted into scientific notation, 2.55 x 105, the 10 is raised to the 5th power of ten. It allows us to compare the order of magnitude of different numbers. For example,

A = 5.4 x 106

B = 5.4 x 108

It shows B is two orders of magnitude larger than A.