# Magnetic force: definition, formula, examples (2023)

• WroteSaurav_C
• Last change 01-25-2023 (Video) Magnetic Force and Magnetic Field | Don't Memorise

The mobility of the charge causes a magnetic force, which results frommagnetic force.Have you ever noticed the force acting on a magnetic compass needle? Do you know how DC/AC motors work? It's all because of the magnetic force.

The interaction of moving electric charges is the fundamental nature of magnetism. Electric forces act on electric charges whether the charges are moving or not, but magnetic forces only act on moving charges and current-carrying wires.

## What is itMagnetic force?

The magnetic force is the result of the electromagnetic force and is caused by the movement of charges. The unknown electric field can be determined by the magnitude and direction of the force on the test charge $$(q)$$ at rest. To investigate the unknown magnetic field (denoted by $$\overrightarrow B$$), we need to measure the magnitude and direction of the force on the moving test charge.
Size:The magnitude of the magnetic force $$(F)$$ on a charge $$(q)$$ moving at a speed $$(v)$$ in a magnetic field of strength $$(B)$$ is given by:
$$\right arrow F = \;qvB\,\sin \theta \,\widehat n$$
where $$θ$$ is the angle between the lines $$v$$ and $$B$$.
Direction:The direction of the magnetic force $$(F)$$ is perpendicular to the plane formed by $$v$$ and $$B$$, and can be easily determined by the right-hand rule. rule of thumb, to determine the direction of the magnetic force on a positive moving charge, the thumb of the right hand should point in the $$v$$ direction, the fingers in the $$B$$ direction, and the $$(F)$$ force is perpendicular on the right palm. And the direction of the force $$(F)$$ on the negative charge is in the opposite direction from the one above (ie, directed from the back of the hand). Two bodies containing a charge of the same direction of motion have a magnetic attraction between them. Similarly, objects with charges moving in opposite directions have a repulsive force between them.

(Video) Magnetism, Magnetic Field Force, Right Hand Rule, Ampere's Law, Torque, Solenoid, Physics Problems

SI unit:The SI unit for the magnitude of the magnetic field strength is called the tesla $$(\rm{T})\, which is equivalent to one Newton per ammeter. Sometimes a smaller unit is taken as the gauss \((10^{-4 }\,\rm{ T})$$.

### Lorentzova sila

When the expression for the magnetic force is combined with the expression for the electric force, the combined expression is known asLorentzova sila.
Let's consider a point charge $$(q)$$ (moving with speed $$v$$ and located at $$r$$ at a given time $$t$$) in the presence of an electric field $$[E (r) ]$$ and the magnetic field $$[B(r)]$$. Now the total force on the electric charge $$(q)$$ due to the electric and magnetic fields can be written as:
$$\overrightarrow F = \;q\left[ {\overrightarrow E \left( r \right) + \overrightarrow v \times \overrightarrow B \left( r \right)} \right] \equiv {\overrightarrow F _ {{\text{elektrisch}}}} + {\overrightarrow F _{{\text{magnetisch}}}}$$

This power was given by the firstHA Lorentzbased on extensive experiments by Ampere et al. During the interaction with the magnetic field, the following features were observed:

1. It depends on the charge $$(q)$$ of the particle, the speed $$(v)$$ and the magnetic field $$(B)$$, and the force on the negative charge is opposite to that on the positive charge.
2. The magnetic force $$\left[ {q\left( {\overrightarrow v \times \overrightarrow B} \right)} \right]$$ consists of the vector product of the velocity and the magnetic field. If the velocity and the magnetic field are parallel or antiparallel, the vector product causes the force due to the magnetic field to become zero. The force acts in a direction perpendicular to both the velocity and the magnetic field. The direction is given by the screw rule or the right-hand rule for the vector (or cross) product, as shown in the figure below.
3. The magnetic force is zero when the charge is not moving (as then $$|v |= 0$$).

### Magnetic force on a current-carrying conductor

When a charged particle is in motion, it experiences a magnetic force in a magnetic field. Similarly, when a current-carrying wire is placed in a magnetic field, it also experiences a force. The wire through which the current flows acted on the magnetic force due to the movement of electrons in it. Let's assume that a conducting wire carrying a current $$\left( i \right)$$ is placed in a magnetic field $$\left({{overrightarrow B} \right)$$.
Consider the minor element $$(dl)$$ of the string shownAfb. (c).Free electrons float with speed $$v_d$$ opposite to the current direction. The relationship between current $$(i)$$ and displacement speed $$(v_d)$$ is,

Afb. (c)

$$i = jA = nev_d A$$ …..(i)
Where $$A$$ is the cross-sectional area of ​​the wire, and $$n$$ is the number of free electrons per unit volume. Each electron experiences an average magnetic force of
$$\overrightarrow f = – e\overrightarrow {{v_d}} \times \overrightarrow B$$
And the number of free electrons in the considered secondary element is $$nAdl$$. Then the magnetic force on the wire of length $$(dl)$$ will be
$$d\right arrow F = \left( {nAdl} \right)\left( { – e\right arrow {{v_d}} \times \right arrow B } \right)$$
If we denote the length $$(dl)$$ along the flow direction by $$d\right arrow {l}$$, the above equation becomes as
$$d\right arrow F = nAe{v_d}d\right arrow {l} \times \right arrow B$$
Using equation (i).
$$d\upper right arrow F = i d\upper right arrow {l} \times \upper right arrow B$$ …….(ii)
The quantity $$i d\overrightarrow {l}$$ is called the current element. If a straight wire of length $$(l)$$ through which a current $$(i)$$ flows is placed in a uniform magnetic field $$\arrow above the right side of B$$, the force on it will be
$$\right arrow F = i\right arrow l \times \right arrow B$$ …….(iii)

### Continue

If a charged particle moves with velocity $$(v)$$ in a magnetic field $$(B)$$, then due to the interaction between the magnetic field produced by the moving charge and the applied magnetic field, the charge $$( q)$$ experiences a magnetic force.
The magnitude of the magnetic force $$(F)$$ on a charge $$(q)$$ moving at a speed $$(v)$$ in a magnetic field of strength $$(B)$$ is given by the expression $$F = qvB$$ sin \,\theta \widehat n\). Where $$θ$$ is the angle between the lines $$v$$ and $$B$$, and the direction of the magnetic force $$(F)$$ is perpendicular to the plane formed by $$v$$ and $$B$$ , and can be easily determined by the right-hand rule.
The Lorentz force is the total force on a charge $$(q)$$ moving with velocity $$(v)$$ in the presence of both magnetic and electric fields. It is given by the expression: $$F = q\left[ {E\left( r \right) + v \times B\left( r \right)} \right].$$
If a straight wire of length $$(l)$$ carrying a current $$(i)$$ is placed in a uniform magnetic field $$(\arrow top right B)\, the force on it is: \( \vertical arrow F = i\right arrow l \times \upper right arrow B$$

(Video) Magnetic Force

### Solved problems

Question 1. A charge of $$2.0\,\rm{μC}$$ moves with a speed of $$2.0 × 10^6 \,\rm{m}\,\rm{s}^{-1 }\ ) along the positive \(x-$$ axis. In space there is a magnetic field $$(\overrightarrow B)$$ of strength $$\left( {0.20\overrightarrow j + 0.40\overrightarrow k } \right){\text{T}}$$. What is the magnetic force acting on the charge?
Sila na teret $$= q\overrightarrow v \times \overrightarrow B$$
$$F = q\right arrow \times \upper right arrow B$$
$$\right arrow F = \left( {2,0 \times {{10}^{ – 6}}{\text{C}}} \right)\left( {2,0 \times {{10} ^6}\; {\text{m}}\;{{\text{s}}^{ – 1}}\;\arrow up right and \;} \right) \times \left( {0,20 \,\arrow up right j + 0.40\, \overrightpijl k } \right){\text{T}}$$
$$\Rightarrow F = 4.0\lijevo( {0.20\,\overrightarrow i \times \overrightarrow j + 0.40\,\overrightarrow i \times \overrightarrow k } \desno){\text{N}}$$
$$\right arrow F = \left( {0,8\,\up arrow k – 1,6\,\up arrow j } \right){\text{N}}.$$

Question 1. How is the magnetic force created?
Magnetic force is created by permanent magnets, electric current or other moving charges. The magnetic force can be both repulsive and attractive.

Question 2. How to find the direction of the magnetic force using the right hand rule?
The right-hand rule states that to find the direction of the magnetic force on a positive moving charge, the thumb of the right hand points in the direction $$v$$, the fingers are in the direction $$B\ ) , and the force \((F)$$ is perpendicular to the right Palm.

V.3. Write the SI unit for magnetic field strength?
The SI unit for the magnitude of magnetic field strength is called the tesla $$(\rm{T})\, which is equivalent to one Newton per ammeter. Instead, the smaller unit is called the gauss \((10^{- 4}\,\rm {T})$$.

(Video) Magnetic force on a proton example (part 1) | Physics | Khan Academy

V.4. What are common examples of magnetic force?
There are many examples of magnetic force such as the attraction and repulsion of two magnets, the force that acts on a compass needle is a magnetic force, the forces that act in DC/AC motors that make them rotate are magnetic forces and magnetic forces are also used in accelerators particle.

V.5. What is this magnetic force?
Magnetic force is an electromagnetic force. It is a field force, magnetic force, attraction or repulsion that occurs between electrically charged particles due to their motion. It is the basic force responsible for effects such as the operation of an electric motor and the attraction of a magnet to iron.

We hope this detailed article on magnetic force will help you in your preparation. If you get stuck, let us know in the comments section below and we will get back to you as soon as possible.

## FAQs

### What is the formula for force in magnetic force? ›

F = qv × B. The force F is perpendicular to the direction of the magnetic field B. It also is perpendicular to the direction of the velocity v.

What are 5 examples of magnetic force? ›

Examples of magnetic force is a compass, a motor, the magnets that hold stuff on the refrigerator, train tracks, and new roller coasters. All moving charges give rise to a magnetic field and the charges that move through its regions, experience a force.

What is the definition of magnetic force and examples? ›

magnetic force, attraction or repulsion that arises between electrically charged particles because of their motion. It is the basic force responsible for such effects as the action of electric motors and the attraction of magnets for iron.

What is magnetic force answers? ›

What is the magnetic force? The magnetic force is a consequence of the electromagnetic force, one of the four fundamental forces of nature, and is caused by the motion of charges. Two objects containing charge with the same direction of motion have a magnetic attraction force between them.

Is magnetic force a force answer? ›

Magnetic force is a contact force.

What are 3 examples of magnetic things? ›

Magnetic poles always exist in pairs. Examples of magnetic substances include iron, nickel, cobalt, stainless steel, and many rare earth metals. Diamagnetic materials like copper and gold are weakly repelled by a magnetic field. Paramagnetic materials like calcium and aluminum are weakly attracted by a magnetic field.

Is magnetic an example of force? ›

Magnetic attraction and repulsion is one of three fundamental non contact forces in nature.

What is magnetic force with example kids? ›

You can feel the magnetic force if you hold two magnets so that their poles are near each other. If the poles are opposite (north and south), you will feel an attraction between the magnets. If the poles are identical (north and north or south and south), you will feel the magnets repelling. each other.

What is an example sentence for magnetic force? ›

1. The iron has lost its magnetic force. 2. The electrically charged gas particles are affected by magnetic forces.

How do you explain magnetic force? ›

Magnetism is the force exerted by magnets when they attract or repel each other. Magnetism is caused by the motion of electric charges. Every substance is made up of tiny units called atoms. Each atom has electrons, particles that carry electric charges.

### What is the formula for the magnetic moment? ›

τ=p×B. The SI unit for magnetic moment is clearly N m T−1. τ=IA×B.

What is an example of a magnetic energy? ›

Some examples of magnetic energy are electric motors, generators, loudspeakers, etc.

What is a magnetic force quizlet? ›

magnetic forces. attract each other materials like iron and similar metals like magnetics like charge. magnetic forces facts. like electric forces react over distance and the more tight knite coils there are the stronger the force is. magnetic poles.

What is the definition of a magnet? ›

What is a Magnet? A magnet is defined as. An object which is capable of producing magnetic field and attracting unlike poles and repelling like poles.

Is magnetic energy a force? ›

Magnetism is a force, but it has no energy of its own,” says David Cohen-Tanugi, vice president of the MIT Energy Club and a John S. Hennessy Fellow in MIT's Materials Science and Engineering department.

What is the force answer? ›

In Physics, force is defined as: The push or pull on an object with mass causes it to change its velocity. Force is an external agent capable of changing a body's state of rest or motion. It has a magnitude and a direction.

What is the 2 formula for force? ›

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

What is the formula of force with example? ›

The force is calculated by the formula. F= m/a where F= applied force on an object, m = mass of the object, and a stands for acceleration.

What 4 materials are magnetic? ›

The most common metals used for permanent magnets are iron, nickel, cobalt and some alloys of rare earth metals.

What is 1 example of a magnetic substance? ›

Only a few metals like iron, nickel and cobalt are magnetic.

### What has magnetic force? ›

A magnet is an example of the magnetic force. Two magnets placed together may attract each other or they may be forced apart, depending on the alignment of the positive and negative charges and spin (also referred to as poles: north and south). This occurs even when magnets are not in motion.

What is an example of a magnetic force with an experiment? ›

Solution: Take a bar magnet and place a steel pin at some distance. Then we observe that nothing happens but when we bring the steel pin near the pole of a bar magnet, we notice that the pin sticks to the poles of the magnet. This experiment shows that maximum magnetic force acts at the poles of the magnet.

What are 5 examples of not magnetic? ›

Rubber, plastic, stainless steel, feather, paper, mica, gold, silver, leather, and other non-magnetic materials are examples.

What are 4 properties of magnets? ›

Some of the properties of a magnet are:
• A magnet has two poles known as North-Pole and South-Pole.
• A magnet, when suspended freely, always rests in a north-south direction.
• A magnet has attractive properties. ...
• Like poles of magnets repel each other whereas unlike poles attract each other.

What are magnets 4th grade? ›

A magnet is a rock or a piece of metal that can pull certain types of metal toward itself. The force of magnets, called magnetism, is a basic force of nature, like electricity and gravity. Magnetism works over a distance. This means that a magnet does not have to be touching an object to pull it.

What is the best example of magnetism? ›

The most familiar example of magnetism is a bar magnet, which is attracted to a magnetic field and can attract or repel other magnets. Ancient people used lodestones, natural magnets made of the iron mineral magnetite.

What is a real life example of magnetism? ›

Magnetic Force Examples

Computer hard drives use magnetism to store the data on a rotating disk. More complex applications include: televisions, radios, microwave ovens, telephone systems, and computers.

What is the magnetic force for Grade 6? ›

Magnetism: a physical phenomenon produced by the motion of electric charge, resulting in attractive and repulsive forces between objects. Poles: each of the two points or regions of an artificial or natural magnet to and from which the lines of magnetic force are directed. Magnets have both north and south poles.

What is the formula for magnetic torque? ›

τ = N I A B sinθ

This is the torque on a current-carrying loop in a uniform magnetic field. This equation can be shown to be valid for a loop of any shape.

What is magnetic length? ›

The shortest distance joining the magnetic poles of a magnet is known as magnetic length.

### What is magnetic moment force? ›

Magnetomotive force, also known as magnetic potential, is the property of certain substances or phenomena that gives rise to magnetic field s. Magnetomotive force is analogous to electromotive force or voltage in electricity.

How do you make magnetic power? ›

Magnetic fields can be used to make electricity

Moving magnetic fields pull and push electrons. Metals such as copper and aluminum have electrons that are loosely held. Moving a magnet around a coil of wire, or moving a coil of wire around a magnet, pushes the electrons in the wire and creates an electrical current.

How does magnetism work for kids? ›

Magnets produce lines of magnetic force which leave a magnet from its north pole and re-enters the magnet at the south pole. When two magnets are placed together one magnet's north pole will attract the other's south pole. However, two north poles or two south poles will always repel each other.

How is magnetic energy made? ›

In magnets, the electrons in atoms at one end all spin in one direction, and those in atoms at the other end all spin the opposite way. This creates a force of energy around the magnet, called a magnetic field.

What are 10 examples of magnetic and non magnetic? ›

Magnetic substances are iron, nickel, and cobalt, as objects made of these materials are attracted by a magnet. Rubber, plastic, stainless steel, feather, paper, mica, gold, silver, leather, and other non-magnetic materials are examples.

What are the different types of magnetic force? ›

Five basic types of magnetism have been observed and classified on the basis of the magnetic behavior of materials in response to magnetic fields at different temperatures. These types of magnetism are: ferromagnetism, ferrimagnetism, antiferromagnetism, paramagnetism, and diamagnetism.

What is an example of magnetic force in nature? ›

Black sand on the beaches of La Ventanilla, Mexico, is magnetized. The iron oxide in the sand is attracted to the strong magnetic field produced by the magnet the man is holding. Magnetism is the force exerted by magnets when they attract or repel each other. Magnetism is caused by the motion of electric charges.

What are the 4 magnetic metals? ›

Magnetic metals include:
• Iron.
• Nickel.
• Cobalt.
• Some alloys of rare earth metals.
Oct 27, 2015

What are the names of 4 magnetic substances? ›

Iron, cobalt, nickel, and other metals are examples.

What are the 3 magnetic force factors? ›

The mathematical factors that determine a magnet's force is the charge and velocity of the particle, the magnetic field, and the sine of the angle between the magnetic field and velocity vectors.

### What are 2 examples of magnetic field? ›

Magnetic Force Examples

A compass detects the Earth's magnetic field. A needle is moved by the magnetic force, so that one end points north and the other end points south. There is a natural magnetic field surrounding us all the time; the Earth's magnetic field.

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