Magnetic Force: Direction, Calculation and Fleming’s Right-Hand Rule

Magnetic force is an attraction or repulsion force that arises due to the motion of the charged particles. Due to this force magnets with opposite poles attracts each other and there is repulsion between magnets if the polarity is the same. 

• All moving charges give rise to a magnetic field or magnetism field and the charges that move through its regions, experience a magnetic force.
•  A compass, the magnets that hold the refrigerator door, a motor, and modern roller coasters are all examples of magnetic force.

Key Terms: Magnetic Force, Charges, Current, Force, Electromagnetic force, Magnets, Magnetic field, Torque, force, Motion, Magnetism field, 

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What Is Magnetic Force?

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The magnetic force is a consequence of the electromagnetic force, one of the four fundamental forces of nature, and it is caused by the motion of charges.

• The main difference between electric force and magnetic force is that electric force acts between all charged particles, whether they are moving or not, while magnetic force acts between moving charged particles.
• The magnetic force between two moving charges can be explained as the effect exerted by a magnetic field upon either charge, created by the other.
• Many natural and artificial objects also possess this magnetic force known as magnets.
• It is found in several experiments that a magnetic field surrounds the moving charges.
• The nature of magnetic force can be attractive or repulsive.
• There is a magnetic attraction between two charges if they are moving in the same direction and there is magnetic repulsion if they are moving in opposite directions.
• Similarly, there is the attractive magnetic force between two unlike poles of magnets and repulsive force between two like poles of magnets.

Magnet

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Calculation of Magnetic Force

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We take the different conditions for calculating magnetic force. Some of these conditions are:

• Magnetic force on moving charge in a magnetic field
• Magnetic force on a current carrying conductor in a magnetic field
• The magnetic force between two parallel current carrying conductor

Magnetic force on moving charge in a magnetic field

Let us assume a uniform magnetic field B in which a positive charge ‘q’ moves, with a velocity v. The angle between v and B, is θ. This charged particle will experience a force depending on the following factors:

• The magnitude of the force exerted on the charge is directly proportional to the charge’s magnitude, i.e., F ∝ q
• The force’s magnitude F is directly proportional to the velocity v and it acts in a direction that is perpendicular to the magnetic field, i.e., F ∝ v Sin θ
• The force’s magnitude F is directly proportional to the magnetic force’s applied magnitude. It is given by: F ∝ B

From the above three points, we get F ∝ qvBSin θ

Now, after we remove the proportionality sign, 

we obtain F = kqvBSin θ

Here, k is a constant having the value of 1, 

therefore the equation becomes,

 F = qvBSin θ or F = q (v x B)

Magnetic Force

Magnetic force on a current carrying conductor in a magnetic field

Consider a conductor of length L carrying current I placed in uniform magnetic field B. Let θ be the angle between the length of the conductor and the uniform magnetic field, and then the magnetic force experienced by the current carrying conductor is given by

F = BILSin θ or F = I (L x B)

If a current loop of area A and having N number of turns is placed in a uniform magnetic field B, then torque on the current loop is given by

\(\tau =NIABsin\theta\)

The above expression gives torque on a current loop in a uniform magnetic field, where I is the current flowing through the loop and θ is the angle between normal to the plane of the loop and the magnetic field.

The magnetic force between two parallel current carrying conductor

Consider two infinitely long parallel conductors carrying current I₁ and I₂ respectively separated by distance d. The magnetic force between the conductors is given by

\(F=\frac{\mu_o}{4 \pi }(\frac{2I_1I_2}{d})\)

If the current is in the same direction in two conductors, then the magnetic force is attractive and if the current is in opposite direction, then the magnetic force is repulsive.

Also Read: Current coil

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The Direction Of Magnetic Force

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The direction of the magnetic force is a cross-product of the magnetic field and velocity, where the magnetic field is perpendicular to the plane containing ‘B’ and ‘v’. 

• Let us take a piece of paper where B and v are in the plane of the paper, then as the Right-handed screw rule method, the direction of F on the particle with a positive charge will be perpendicular to the paper’s plane upwards. 
• However, on the particle with a negative charge, the direction changes downward.

We can see the diagram of the right-hand rule or right-hand screw for both positive and negatively charged particles below:

Right-Hand Rule 

Also Read: Magnetism Formula

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Fleming's Right-Hand Rule

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The fleming’s right-hand rule is as specified below:

• The Right-hand rule can be used to calculate the force`s trajectory (F).
• It refers to gadgets that produce currents through shifting in a magnetic field.
• Place your index finger alongside the charge v direction of motion.
• Between v and B, rotate your centre finger far from your index finger.
• Maintain a perpendicular angle between your thumb and the plane created through your index and centre fingers.
• If the charge q is positive, your thumb will point withinside the direction of the force (F).

Fleming's Right-Hand Rule

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Things To Remember

• Magnetic force is a force of attraction or repulsion.
• Electric force acts between all charged particles, whether they are moving or not, while magnetic force acts between moving charged particles.
• A magnetic field surrounds the moving charges. 
• Magnetic force is a direct consequence of electromagnetic force.
• Many natural and artificial objects possess magnetic force.
• Fleming’s right-hand rule is used to calculate the traditional current flow.

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Previous Year Questions

1. Work done in turning a magnet of magnetic moment M by an angle of 90? from the mgnetic meridian is n times the corresponding work done to turn through an angle of 60?, where n is...[BCECE 2019]
2. The area enclosed by the loop is A. If there are nn turns in the loop, the torque acting on the loop is given by...[VITEEE 2011]
3. The magnetic Lorentz force experienced by a charge q, entering a magnetic field B with a velocity v is...[KCET 2009]
4. A current of 1A is flowing on the sides of an equilateral triangle of sides 4.5×10⁻²m. The magnetic field at the centroid of the triangle is...[BHU UET]
5. A charged particle moves through a magnetic field perpendicular to its direction. Then..​
6. Force of attraction or repulsion between two current carrying wires separated by a distance r is proportional to​
7. An electron projected in a perpendicular uniform magnetic field of 3×10⁻³T moves in a circle of radius 4 mm. The linear momentum of electron (inkg−ms−1)is
8. If the speed of the electron is doubled and the magnetic field is halved the resulting path would have a radius:​
9. The magnitude of the force due to the magnetic field acting on the charge at this instant is​
10. The magnetic force on a point charge is →F=q(→V×→B) Here, q= electric charge →V= velocity of point charge →B=magnetic Held The dimension of →Bis :
11. The electric charge, in uniform motion, produces​
12. Let a , b and c be the ratio of their time periods, radii and pitches of the helical paths then:
13. The normal to the plane of coil makes an angle 30∘ with the magnetic field. The flux through the coil is...[KCET 2015]
14. If a proton of mass 1.8×10²⁷kg was to move in a circle of same radius in the same magnetic field, then its speed will become...[VITEEE 2015]​
15. If the specific charge of the electron is 1.7×10¹¹C/kg. The radius of the circular nath will he...[BITSAT 2005]
16. In the presence of magnetic field ?B? and electric field ?E?, the total force on a moving charged particle is...[VITEEE 2006]
17. Calculate the magnitude of the force experienced by the electron at that instant...[NEET 2021]
18. The magnetic force acting on a charged particle of charge −2μC in a magnetic field of 2T acting in y direction, when the particle velocity is is (2^i+3^j)×10⁶ms⁻¹..[NEET 2009]
19. The force on the charge Q is...[NEET 2010]
20. Two parallel wires in free space are 10 cm apart and each carries a current of 10 A in the same direction. The force exerted by one wire on the other, per metre length is..[NEET 1997]