**Magnetic force **(F) is defined by the lorentz force law. Using the equation of magnetic force: **F = q v B sinθ**, the value of magnetic force acting on a particle can be calculated.

Here’s the equation of magnetic force:

- Magnetic force acting on a moving charge,
**F = q v B sinθ**

- Magnetic force acting on a current carrying wire,
**F = I L B sinθ**

Where,

I = electric current, A

L = length of a wire, m

Let’s solve some problems based on these equations, so you’ll get a clear idea.

## Magnetic Force Practice Problems

**Problem 1:** A particle with a charge of 6 µC is moving at 1.5 × 10^{6} m/s perpendicularly through a magnetic field with a strength of 0.5 T. Calculate the magnetic force acting on a particle.

Solution:

Given data:

Charge of a moving particle, q = 6 µC = 6 × 10^{-6} C

Velocity of a particle, v = 1.5 × 10^{6} m/s

Magnetic field, B = 0.5 T

Angle between velocity vector and magnetic field vector, θ = 90°

Magnetic force acting on a particle, F = ?

Using the equation of magnetic force, (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:** A 15 cm wire with a current of 4 A is oriented at an angle 45° from parallel to a magnetic field with a strength of 5 T. What is the magnetic force acting on a wire?

Solution:

Given data:

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

Magnetic force acting on a wire, F = ?

Using the equation of magnetic force, (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:** Calculate 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 36° from perpendicular through a magnetic field.

Solution:

Given data:

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°

Magnetic force acting on a particle, F = ?

Using the equation of magnetic force, (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:** A 10 cm wire with a current of 9 A is oriented at an angle 25° from parallel to a magnetic field with a strength of 12 T. Calculate the magnetic force acting on a wire.

Solution:

Given data:

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

Magnetic force acting on a wire, F = ?

Using the equation of magnetic force, (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**.

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**Related:**

- Force Equation
- Normal Force Equation
- Net Force Formula
- Applied Force Formula
- Centripetal Force Equation
- Centrifugal Force Equation
- Spring Force Equation
- Tension Force Formula
- Electric Force Equation

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