Magnetic Flux Density Formula

What is Magnetic Flux Density?

Definition: Magnetic flux density is the magnetic flux per unit area in a magnetic field.

We use B to denote magnetic flux density.

The formula for magnetic flux density is

Magnetic field (B) = Magnetic flux (Φ) / Area (A)

This implies that

B = Φ / A

After cross-multiplying the above equation, we have

Φ = BA

The other units we use to measure magnetic flux density are wb/m², Tesla(T), and gauss.

Magnetic force (F): Whenever a charge is moving in a magnetic field, it experiences a force which is also called magnetic force.

The formula for magnetic force is

F = IBSinθ

and I = QV

Which shows that

F = QVBSinθ

For force carrying conductors in a magnetic field, we have

F = IBLSinθ or F = QVBLSinθ

How to Calculate Magnetic Flux Density

Problem

The magnetic flux density of a 10m long stiff wire carrying a current of 4A is 0.8T. Calculate the force if it is lying in a direction at 60⁰ to the magnetic field.

Solution

Data: We retrieve our data from the above question

Length (L) = 10m

Current (I) = 4A

Magnetic flux (Φ)= 0.8T

Force (F) = ?

Angle (θ) = 60⁰

and the formula to use is F = IBLSinθ

Thus, by substituting our data into the above formula we have

F = 4 x 0.8 x 10 x Sin60⁰

F = 32 x 0.866

Therefore, the final answer is 27.712

F = 27.712N

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