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Magnetism Formula Calculator

\[ F = q v B \sin(\theta) \]

1. What is the Magnetism Formula Calculator?

Definition: This calculator computes the magnetic force (\(F\)) on a charged particle moving in a magnetic field, using the Lorentz force formula \( F = q v B \sin(\theta) \), where \(q\) is the charge, \(v\) is the velocity, \(B\) is the magnetic field strength, and \(\theta\) is the angle between the velocity and magnetic field vectors.

Purpose: It is used in electromagnetism to determine the force on charged particles in magnetic fields, applicable in particle physics, electronics, and magnetic field studies.

2. How Does the Calculator Work?

The calculator uses the Lorentz force formula for magnetic fields:

Formula: \[ F = q v B \sin(\theta) \] where:

  • \(F\): Magnetic force (N, kN, lbf)
  • \(q\): Charge (C, mC, µC)
  • \(v\): Velocity (m/s, km/h, mph, ft/s)
  • \(B\): Magnetic field (T, mT, G)
  • \(\theta\): Angle (rad, deg)

Unit Conversions:

  • Charge:
    • 1 C = 1 C
    • 1 mC = 0.001 C
    • 1 µC = 0.000001 C
  • Velocity:
    • 1 m/s = 1 m/s
    • 1 km/h = \( \frac{1000}{3600} \) m/s \(\approx 0.27777777778 \, \text{m/s}\)
    • 1 mph = 0.44704 m/s
    • 1 ft/s = 0.3048 m/s
  • Magnetic Field:
    • 1 T = 1 T
    • 1 mT = 0.001 T
    • 1 G = 0.0001 T
  • Angle:
    • 1 rad = 1 rad
    • 1 deg = \( \frac{\pi}{180} \) rad \(\approx 0.01745329252 \, \text{rad}\)
  • Magnetic Force (Output):
    • 1 N = 1 N
    • 1 kN = 1000 N
    • 1 lbf = 4.4482216152605 N
The magnetic force is calculated in newtons (N) and can be converted to the selected output unit (N, kN, lbf). Results greater than 10,000 or less than 0.001 are displayed in scientific notation; otherwise, they are shown with 4 decimal places.

Steps:

  • Enter the charge (\(q\)), velocity (\(v\)), magnetic field (\(B\)), and angle (\(\theta\)) with their units (default: \(q = 1.6 \times 10^{-19} \, \text{C}\), \(v = 1000 \, \text{m/s}\), \(B = 1 \, \text{T}\), \(\theta = 90^\circ\)).
  • Convert inputs to SI units (C, m/s, T, rad).
  • Validate that velocity and magnetic field are non-negative, and angle is within the appropriate range (0 to 360° or 0 to \(2\pi\) rad).
  • Calculate the magnetic force in newtons using the formula.
  • Convert the magnetic force to the selected output unit.
  • Display the result, using scientific notation if the value is greater than 10,000 or less than 0.001, otherwise rounded to 4 decimal places.

3. Importance of Magnetic Force Calculation

Calculating magnetic force is crucial for:

  • Particle Physics: Understanding the motion of charged particles in magnetic fields, such as in particle accelerators or cosmic rays.
  • Electronics: Designing devices like electric motors, generators, and magnetic sensors where magnetic forces play a key role.
  • Education: Teaching the principles of electromagnetism and the Lorentz force in physics.

4. Using the Calculator

Examples:

  • Example 1: Calculate the magnetic force for \(q = 1.6 \times 10^{-19} \, \text{C}\), \(v = 1000 \, \text{m/s}\), \(B = 1 \, \text{T}\), \(\theta = 90^\circ\), output in N:
    • Enter \(q = 1.6 \times 10^{-19} \, \text{C}\), \(v = 1000 \, \text{m/s}\), \(B = 1 \, \text{T}\), \(\theta = 90^\circ\).
    • Convert: \(\theta = 90 \times \frac{\pi}{180} = \frac{\pi}{2} \, \text{rad}\).
    • Angle factor: \(\sin(\theta) = \sin(\frac{\pi}{2}) = 1\).
    • Magnetic force: \(F = 1.6 \times 10^{-19} \times 1000 \times 1 \times 1 = 1.6 \times 10^{-16} \, \text{N}\).
    • Output unit: N (no conversion needed).
    • Result: \( \text{Magnetic Force} = 1.6000 \times 10^{-16} \, \text{N} \).
  • Example 2: Calculate the magnetic force for \(q = 1 \, \text{mC}\), \(v = 3600 \, \text{km/h}\), \(B = 10000 \, \text{G}\), \(\theta = 1.5708 \, \text{rad}\), output in lbf:
    • Enter \(q = 1 \, \text{mC}\), \(v = 3600 \, \text{km/h}\), \(B = 10000 \, \text{G}\), \(\theta = 1.5708 \, \text{rad}\).
    • Convert: \(q = 1 \times 0.001 = 0.001 \, \text{C}\), \(v = 3600 \times \frac{1000}{3600} = 1000 \, \text{m/s}\), \(B = 10000 \times 0.0001 = 1 \, \text{T}\).
    • Angle factor: \(\sin(\theta) = \sin(1.5708) \approx 1\).
    • Magnetic force in N: \(F = 0.001 \times 1000 \times 1 \times 1 = 1 \, \text{N}\).
    • Convert to output unit (lbf): \(1 \times \frac{1}{4.4482216152605} \approx 0.2248 \, \text{lbf}\).
    • Result: \( \text{Magnetic Force} = 0.2248 \, \text{lbf} \).

5. Frequently Asked Questions (FAQ)

Q: What is the magnetic force?
A: The magnetic force is the force exerted on a charged particle moving in a magnetic field, as described by the Lorentz force equation \( F = q v B \sin(\theta) \). It acts perpendicular to both the velocity and magnetic field vectors.

Q: Why must velocity and magnetic field be non-negative?
A: In this context, velocity and magnetic field strength are magnitudes (scalar quantities), so they must be non-negative. The direction of the force is determined by the right-hand rule, but this calculator computes the force magnitude.

Q: What does the angle \(\theta\) represent?
A: The angle \(\theta\) is the angle between the velocity vector of the charged particle and the magnetic field vector. Maximum force occurs when \(\theta = 90^\circ\) (\(\sin(\theta) = 1\)), and zero force occurs when \(\theta = 0^\circ\) or \(180^\circ\) (\(\sin(\theta) = 0\)).

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