Magnetic Force Equation | Problems (And Solutions)

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Magnetic Force Equation

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:

  1. Magnetic force acting on a moving charge, F = q v B sinθ
  1. 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 × 106 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 × 106 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 × 106 × 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 × 107 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 × 107 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 × 107 × 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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