Magnetism

Magnetism is a physical phenomenon arising from the intrinsic properties of certain materials. It manifests as the ability of magnets to exert attractive or repulsive forces on other objects without physical contact. Magnets typically possess two poles, north and south, which interact according to specific rules: opposite poles attract, while like poles repel. For instance, when a magnet approaches a refrigerator door, the magnetic attraction pulls it toward the metal surface. The study of magnetism encompasses various phenomena, including the behavior of magnetic fields, the properties of magnetic materials, and their applications in technology and everyday life.

Magnetic force refers to the force exerted by magnets or magnetic fields on other magnetic materials or moving charges. It is analogous to the electric force in electrostatics. Mathematically, the equation for the magnetic force (F) acting on a charge (q) moving with velocity (v) in a magnetic field (B) is given by:

$$F = qvBsin\theta$$

where θ is the angle between the velocity vector and the magnetic field vector.

When a current (I) flows through a wire, it generates a magnetic field around the wire. The force (F) experienced by a current-carrying wire of length (l) in a magnetic field (B) is given by the equation:

$$F = IlBsin\theta$$

where θ is the angle between the current direction and the magnetic field direction.

Contents

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 × 106 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 × 106 m/s

Applying the formula, 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

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 × 107 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 × 107 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 × 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

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.