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The **magnetic force equation**, derived from the Lorentz force, calculates the magnetic force (F) acting on a charged particle. For a moving charge, the equation is F = q v B sinθ, where q represents the charge, v is the velocity, B is the magnetic field, and θ is the angle between the velocity vector and the magnetic field vector.

For a current-carrying wire, the magnetic force equation is expressed as F = I L B sinθ, where I denotes the electric current flowing through the wire, L represents the length of the wire, B is the magnetic field, and θ is the angle between the wire and the direction of magnetic field.

## Practice problems

### Problem #1

Find the magnetic force acting on a particle with a charge of 6 µC as it moves perpendicular to a magnetic field with a strength of 0.5 T at a velocity of 1.5 × 10^{6} m/s.

**Solution**

Given data:

- Magnetic force acting on a particle, F = ?
- Charge of a moving particle, q = 6 µC = 6 × 10
^{-6}C - Angle between velocity vector and magnetic field vector, θ = 90°
- Magnetic field, B = 0.5 T
- Velocity of a particle, v = 1.5 × 10
^{6}m/s

Applying the formula, for a moving charge:

- F = q v B sinθ
- F = 6 × 10
^{-6}× 1.5 × 10^{6}× sin (90°) - F = 6 × 1.5 × 1
- F = 9 N

Therefore, the magnetic force acting on a particle is **9 N**.

### Problem #2

Determine the magnetic force acting on a 15 cm wire with a current of 4 A that is oriented at a 45° angle from parallel to a magnetic field with a strength of 5 T.

**Solution**

Given data:

- Magnetic force acting on a wire, F = ?
- Length of a wire, L = 15 cm = 0.15 m
- Electric current, I = 4 A
- Wire is oriented from parallel at an angle, θ = 45°
- Magnetic field, B = 5 T

Applying the formula, for a current-carrying wire:

- F = I L B sinθ
- F = 4 × 0.15 × 5 × sin (45°)
- F = 3 × 0.7071
- F = 2.12 N

Therefore, the magnetic force acting on a wire is **2.12 N**.

### Problem #3

Find the magnetic force experienced by a 7 µC charge moving at 5.1 × 10^{7} m/s through a magnetic field with a strength of 10 T at an angle of 36° from perpendicular to the magnetic field.

**Solution**

Given data:

- Magnetic force acting on a particle, F = ?
- Charge of a moving particle, q = 7 µC = 7 × 10
^{-6}C - Velocity of a particle, v = 5.1 × 10
^{7}m/s - Magnetic field, B = 10 T
- Charge moves from perpendicular at an angle, θ = 36°

Applying the formula, for a moving charge:

- F = q v B sinθ
- F = 7 × 10
^{-6}× 5.1 × 10^{7}× sin (36°) - F = 7 × 5.1 × 10 × 0.5877
- F = 209.80 N

Therefore, a moving charge experiences the magnetic force of **209.80 N**.

### Problem #4

Calculate the magnetic force acting on a 10 cm wire with a current of 9 A that is oriented at a 25° angle from parallel to a magnetic field with a strength of 12 T.

**Solution**

Given data:

- Magnetic force acting on a wire, F = ?
- Length of a wire, L = 10 cm = 0.1 m
- Electric current, I = 9 A
- Wire is oriented from parallel at an angle, θ = 25°
- Magnetic field, B = 12 T

Applying the formula, for a current-carrying wire:

- F = I L B sinθ
- F = 9 × 0.1 × 12 × sin (25°)
- F = 10.8 × 0.4226
- F = 4.56 N

Therefore, the magnetic force acting on a wire is **4.56 N**.

## Related

- Force equation
- Normal force equation
- Net force formula
- Applied force formula
**Magnetic force equation**- Centripetal force equation
- Centrifugal force equation
- Spring force equation
- Tension force formula
- Electric force equation

## External links

- The magnetic force on a moving charge – University of Tennessee, Knoxville
- Magnetic forces – HyperPhysics Concepts
- Magnetic force on a current carrying wire – Khan Academy
- Force between magnets – Wikipedia
- 5.3 Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field – Texas Gateway
- 11.5: Magnetic Force on a Current-Carrying Conductor – Physics LibreTexts
- How to Calculate the Magnetic Force at an Angle to a Charge – Study.com
- Magnetic Force: Definition, Equation & Units (w/ Examples) – Sciencing
- Lorentz force | Equation, Properties, & Direction – Britannica
- Lesson Explainer: Force on Conducting Wires in Magnetic Fields – Nagwa Limited
- Magnetic Force – University of Oxford
- Magnetic Force on a Current-Carrying Conductor | Physics – Lumen Learning
- AP Physics 2 : Magnetic Force – Varsity Tutors
- Magnetic Force by Ron Kurtus – Physics Lessons – School for Champions
- Magnetic forces and the magnetic field – Utah State University
- Magnetic Force Formula (Charge-Velocity) – SoftSchools.com
- How would you determine the magnitude of the magnetic force on a 120m length of line? – Socratic
- Magnetic Force: Definition, Equation, and Examples – Science Facts
- Lorentz Force Calculator – Lorentz Calculator

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.