Magnetic Force on Current Wire Calculator
Free calculate force on current-carrying wire in magnetic field using f = bil sin(θ). Get instant, accurate results with our easy-to-use calculator.
Input Parameters
90° = perpendicular (maximum force), 0° = parallel (zero force)
Results
Enter parameters to calculate
What is the Magnetic Force on a Wire?
A current-carrying wire placed in a magnetic field experiences a force. This is the basis for how electric motors work - current in a wire loop in a magnetic field produces torque that rotates the motor.
The force is maximum when the wire is perpendicular to the magnetic field (θ = 90°) and zero when parallel (θ = 0°). The force direction is perpendicular to both the current direction and the magnetic field (right-hand rule).
This force is fundamental in motors, generators, loudspeakers, and many electromagnetic devices. It's also the principle behind the definition of the magnetic field unit (Tesla) and current measurement using force balances.
Magnetic Force Formula
Where:
- • F = Magnetic force (N)
- • B = Magnetic field strength (T)
- • I = Current (A)
- • L = Wire length (m)
- • θ = Angle between wire and field (degrees)
Direction: Perpendicular to both current and field (right-hand rule)
Maximum force: When θ = 90° (perpendicular), F = BIL
How to Calculate
-
1
Convert all units to SI
Convert magnetic field to Tesla, current to amperes, length to meters, angle to radians if needed.
-
2
Calculate sin(θ)
Convert angle to radians: θ_rad = θ_deg × π/180, then calculate sin(θ_rad).
-
3
Calculate force
F = B × I × L × sin(θ). Multiply all four values together.
Practical Examples
Example 1: Perpendicular Wire
B = 0.1 T, I = 5 A, L = 0.5 m, θ = 90° (perpendicular).
Solution:
F = 0.1 × 5 × 0.5 × sin(90°) = 0.1 × 5 × 0.5 × 1
F = 0.25 N (maximum force)
Example 2: Angled Wire
Same parameters but θ = 30°.
Solution:
F = 0.1 × 5 × 0.5 × sin(30°) = 0.1 × 5 × 0.5 × 0.5
F = 0.125 N (half the maximum force)
Applications
Electric Motors
Force on current loops in magnetic fields produces torque, causing motor rotation. This is how all electric motors work.
Loudspeakers
Voice coil (current-carrying wire) in permanent magnet field experiences force, moving the cone to produce sound.
Generators
Understanding force on conductors helps design generators and understand electromagnetic induction principles.
Education
Teaching electromagnetic forces, understanding motor principles, and demonstrating right-hand rule applications.
Frequently Asked Questions
What is the right-hand rule for force direction?
Point fingers in direction of current, curl toward magnetic field direction. Thumb points in direction of force. Alternatively: F = I×L × B (cross product).
Why is force zero when wire is parallel to field?
When θ = 0° (parallel), sin(0°) = 0, so F = 0. The current and field are in the same direction, so there's no perpendicular component to produce force.
How does this relate to motors?
In a motor, current loops in a magnetic field experience forces. These forces create torque that rotates the motor shaft. F = BIL is the force on each wire segment.
What if the wire is curved or not straight?
For curved wires, integrate F = ∫ BIL sin(θ) dl along the wire path. For uniform field and straight wire, the simple formula applies directly.
Can the force do work?
Yes! Unlike magnetic force on moving charges (which is always perpendicular to velocity), force on a wire can do work if the wire moves. This is how motors convert electrical to mechanical energy.