Magnetic force: definition, formula, examples (2023)

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 \(|v |= 0\)).

(Video) Magnetic Force on a Moving Charge In a Magnetic Field

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: \( \vertical arrow F = i\right arrow l \times \upper right arrow B \)

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?
answer:Sila na teret \(= q\overrightarrow v \times \overrightarrow B\)
\(F = q\right arrow \times \upper right arrow B \)
\(\right arrow F = \left( {2,0 \times {{10}^{ – 6}}{\text{C}}} \right)\left( {2,0 \times {{10} ^6}\; {\text{m}}\;{{\text{s}}^{ – 1}}\;\arrow up right and \;} \right) \times \left( {0,20 \,\arrow up right j + 0.40\, \overrightpijl k } \right){\text{T}}\)
\(\Rightarrow F = 4.0\lijevo( {0.20\,\overrightarrow i \times \overrightarrow j + 0.40\,\overrightarrow i \times \overrightarrow k } \desno){\text{N}}\)
\( \right arrow F = \left( {0,8\,\up arrow k – 1,6\,\up arrow j } \right){\text{N}}.\)

Frequently asked questions

Question 1. How is the magnetic force created?
answer: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?
answer: 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?
answer: 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 \((10^{- 4}\,\rm {T})\).

V.4. What are common examples of magnetic force?
answer: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?
answer: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.

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