How to Calculate the Force in a Solenoid

Written by douglas quaid
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How to Calculate the Force in a Solenoid
A solenoid is made from a coil of wire, like this inductor. (drosselspule, induction coil image by Sascha Zlatkov from

A solenoid is an electromagnet made by passing current through a coiled wire. If there is a metal core in the centre of the loop, the magnetic field can exert a force on it which causes it to move forwards or backwards through the loop, depending on the polarity of the magnetic field. Solenoids have a huge variety of applications. The starter relay in your car is a solenoid that uses a small current from the battery to move a switch, which relays the large current needed to start the engine.

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  1. 1

    Determine the magnetic permeability of the core of the solenoid. The core is the material in the centre of the loop. Most materials, including air, have a permeability that's close to the magnetic constant, μ = 4π x 10^-7. Ferromagnetic materials such as nickel or magnetic iron have higher permeability. Magnetic iron, for example, has a permeability of 200.

  2. 2

    Calculate the strength of the magnetic field at the centre of the solenoid. The strength of the magnetic field is given by the equation B = knI, where:

    B = magnetic field in units of Tesla

    k = the magnetic permeability of the core, as determined in Step 1

    n = turn density = number of turns / length of solenoid (in meters)

    I = current in solenoid (in amperes)

  3. 3

    Calculate the force exerted with the equation F = qvB.

    F = force in Newtons

    q = charge of point particle in coulombs

    v = velocity of point particle

    B = magnetic field strength calculated in Step 1

    Both v and B are vectors, amounts that have both a magnitude and direction. To understand vectors, consider the difference between position and velocity. Position has no direction, it just indicates where you are. Velocity, however, is a vector that considers both your speed and the direction you're travelling in.

    The above equation is valid when vectors v and B are perpendicular. In this case, force, F, is a vector that is perpendicular to both v and B. However, when v and B are not perpendicular, the equation is:

    F = qvB x sinθ, where θ (theta) is the angle between v and B, and is less than 180 degrees.

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