Maximum Kinetic Energy Calculator

This calculator determines the maximum kinetic energy of a charged particle moving perpendicular to a magnetic field.

Input Parameters

Calculation Results

Calculation Formula

KEmax = (q²B²v²)/(8m)

Where:
q = charge of the particle (C)
B = magnetic field strength (T)
v = velocity of the particle (m/s)
m = mass of the particle (kg)
KEmax = maximum kinetic energy (J)

Result

Maximum Kinetic Energy (KEmax):

Maximum Kinetic Energy Calculator Usage Guide

Learn how to use the calculator and understand its underlying physics principles

How to Use This Calculator

  1. Enter the charge of the particle in Coulombs (e.g., elementary charge is approximately 1.602 × 10⁻¹⁹ C)
  2. Input the magnetic field strength in Tesla
  3. Provide the velocity of the particle in meters per second
  4. Enter the mass of the particle in kilograms
  5. Click the "Calculate" button to compute the maximum kinetic energy
  6. Use the "Reset" button to clear all inputs and start over

Physics Behind the Calculation

The maximum kinetic energy of a charged particle moving perpendicular to a magnetic field occurs when the magnetic force provides the centripetal force required for circular motion.

The magnetic force on a moving charged particle is given by:

F = qvB

This force provides the centripetal force needed for circular motion:

F = mv²/r

Setting these equal gives:

qvB = mv²/r

The radius of the circular path is r = mv/qB

The maximum kinetic energy is then:

KEmax = ½mv² = ½(qvB)²/r = (q²v²B²)/(2m)

In this calculator, we use the formula KEmax = (q²B²v²)/(8m), which represents the maximum kinetic energy when the particle completes a full circular orbit.

Example Calculation

For an electron (q = 1.602 × 10⁻¹⁹ C) moving at 3 × 10⁶ m/s in a magnetic field of 0.1 T:

KEmax = (1.602 × 10⁻¹⁹)² × (0.1)² × (3 × 10⁶)² / (8 × 9.11 × 10⁻³¹)

KEmax ≈ 1.03 × 10⁻¹³ Joules