Force on Charges and Currents
Lorentz force, cyclotron motion, force between parallel conductors and torque on a loop. (Physics › Magnetic Effects of Current and Magnetism, NEET UG syllabus.)
What is Force on Charges and Currents?
The total force experienced by a charged particle moving in both electric and magnetic fields. It is the vector sum of the electric force (qE) and the magnetic force (q(v x B)).
Key formula / rule: Lorentz Force on a moving charge
Key points
- Calculate the magnetic force on a moving charge and a current-carrying conductor.
- Determine the direction of magnetic force using vector cross product or Fleming's Left-Hand Rule.
- Analyze the motion of a charged particle in a uniform magnetic field.
- Derive and apply the formula for force between two parallel current-carrying conductors.
Common exam trap
Confusing the direction of force, velocity, and magnetic field, especially with cross products or Fleming's rules.
Definitions
- Term
Lorentz Force
- Meaning
The total force experienced by a charged particle moving in both electric and magnetic fields. It is the vector sum of the electric force (qE) and the magnetic force (q(v x B)).
- Term
Magnetic Force
- Meaning
The force experienced by a moving electric charge or a current-carrying conductor when placed in a magnetic field.
- Term
Magnetic Field
- Meaning
A region around a magnetic material or a moving electric charge within which the force of magnetism acts.
- Term
Magnetic Dipole Moment
- Meaning
A measure of the strength and orientation of a magnetic source, such as a current loop or a bar magnet. For a current loop, M = NIA.
- Term
Cyclotron
- Meaning
A particle accelerator that uses a rapidly alternating electric field and a constant magnetic field to accelerate charged particles in an outward spiral path.
Learning objectives
Calculate the magnetic force on a moving charge and a current-carrying conductor.
Determine the direction of magnetic force using vector cross product or Fleming's Left-Hand Rule.
Analyze the motion of a charged particle in a uniform magnetic field.
Derive and apply the formula for force between two parallel current-carrying conductors.
Calculate the magnetic dipole moment of a current loop and the torque it experiences in a magnetic field.
Understand the working principle of a cyclotron.
Formulae
- Name
Lorentz Force on a moving charge
- Note
Vector form, where q is charge, v is velocity, B is magnetic field. Direction by right-hand rule.
- Expression
F = q(v x B)
- Name
Magnitude of Lorentz Force
- Note
θ is the angle between velocity vector (v) and magnetic field vector (B).
- Expression
F = qvB sinθ
- Name
Force on a current-carrying conductor
- Note
Vector form, where I is current, L is length vector in current direction, B is magnetic field. Direction by right-hand rule.
- Expression
F = I(L x B)
- Name
Magnitude of Force on a current-carrying conductor
- Note
θ is the angle between length vector (L) and magnetic field vector (B).
- Expression
F = ILB sinθ
- Name
Radius of circular path of charge in B-field
- Note
For a charge moving perpendicular to a uniform magnetic field.
- Expression
r = mv / (qB)
- Name
Time period of circular path
- Note
For a charge moving perpendicular to a uniform magnetic field.
- Expression
T = 2πm / (qB)
- Name
Frequency of circular path (Cyclotron frequency)
- Note
For a charge moving perpendicular to a uniform magnetic field.
- Expression
f = qB / (2πm)
- Name
Force per unit length between two parallel conductors
- Note
μ₀ is permeability of free space, I₁ and I₂ are currents, d is separation. Attractive if currents are in same direction, repulsive if opposite.
- Expression
F/L = (μ₀ * I₁ * I₂) / (2πd)
- Name
Magnetic dipole moment of a current loop
- Note
N is number of turns, I is current, A is area of the loop. A is a vector normal to the loop, direction by right-hand thumb rule.
- Expression
M = NIA
- Name
Torque on a current loop
- Note
Vector form, where M is magnetic dipole moment, B is magnetic field. Tends to align M with B.
- Expression
τ = M x B
- Name
Magnitude of Torque on a current loop
- Note
θ is the angle between the magnetic dipole moment vector (M) and the magnetic field vector (B).
- Expression
τ = NIAB sinθ
Prerequisites
Basic vector algebra, especially cross product.
Understanding of electric current and magnetic fields.
Knowledge of centripetal force and circular motion.
Concept of magnetic field lines and their properties.
Common mistakes
Confusing the direction of force, velocity, and magnetic field, especially with cross products or Fleming's rules.
Incorrectly applying the right-hand rule for cross products (v x B or L x B).
Forgetting that magnetic force does no work, so speed remains constant in a pure magnetic field.
Mixing up attractive and repulsive forces between parallel conductors.
Not considering the angle 'θ' correctly in magnitude calculations (sinθ).
Using 'L' as scalar length instead of vector 'L' in F = I(L x B).
Keywords
Lorentz force
Magnetic force
Current loop
Magnetic field
Cross product
Cyclotron
Magnetic moment
Torque
Fleming's Left-Hand Rule
Parallel conductors
Practice preview
Which of the following expressions correctly represents the magnetic force F acting on a current-carrying conductor of length L placed in a uniform magnetic field B, where I is the current flowing through the conductor?…
easy
An electron (charge e, mass m) enters a uniform magnetic field B with a velocity v perpendicular to the field. If the electron completes one full revolution in time T, what is the radius of its circular path?…
medium
A proton enters a uniform magnetic field perpendicularly. What is the direction of the magnetic force acting on the proton if its velocity is towards the east and the magnetic field is directed vertically upwards?…
easy