C
CraftExam
medium difficulty10 min

Magnetic Flux Through a Surface

Magnetic flux through a surface is the measure of the magnetic field passing normally through that surface. For a uniform magnetic field, it is given by PhiB = B A cos θ.

In one line: Flux counts the magnetic field crossing the surface normally; normal crossing gives maximum flux.

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Understand it

Magnetic flux depends on three things: magnetic field strength B, area A, and the angle θ between the magnetic field and the area vector. The area vector is perpendicular to the surface. Flux is maximum when the field is perpendicular to the surface and zero when the field is parallel to the surface.

Example

If a coil is kept with its plane perpendicular to a magnetic field, its area vector is parallel to the field, so θ = 0 degrees and flux is maximum: PhiB = BA.

Formula and rule

Formula: PhiB = B A cos θ.

Here PhiB is magnetic flux in weber (Wb), B is the magnetic field or magnetic flux density in tesla (T), A is the surface area in square metre (m2), and θ is the angle between B and the area vector, not the plane of the coil.

The term B cos θ is the component of magnetic field normal to the surface, so the formula measures only the field crossing the surface normally.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A circular coil of area 0.020 m2 is placed in a uniform magnetic field of 0.50 T.

  1. 1If the area vector makes an angle of 60 degrees with the field, PhiB = B A cos θ = 0.50 × 0.020 x cos 60 degrees = 0.010 × 0.5 = 0.005 Wb.
  2. 2The flux linked with the coil is 5.0 × 10−3 Wb.

Method you can reuse

  1. 1Identify B, A, and the correct angle with the area vector.
  2. 2Convert units to tesla and square metre.
  3. 3Substitute in PhiB = BA cos θ.
  4. 4State the answer in weber and mention whether flux is maximum, reduced, or zero.

Visual tip

A useful diagram shows a flat loop, magnetic field lines, the normal to the loop as the area vector A, and the angle θ between B and A. Marking θ with the plane instead of the normal causes wrong answers.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

When is magnetic flux through a flat coil maximum in a uniform magnetic field?

Think first, then show answer
Magnetic flux is maximum when the area vector of the coil is parallel to the magnetic field, which means the plane of the coil is perpendicular to the field. Then θ = 0 degrees and PhiB = BA.

Common wrong answer

Using sin θ directly because the angle is given with the plane, or writing the SI unit as tesla metre instead of weber.

Don't mix this up

Students often take θ as the angle between the magnetic field and the plane of the coil. In the formula PhiB = BA cos θ, θ is the angle between magnetic field and area vector, not the plane.

Exam tip

Always identify the area vector first. If the question gives the angle with the plane, convert it to the angle with the normal before substituting in BA cos θ.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask for flux calculation, maximum or zero flux condition, unit of flux, or the effect of rotating a coil in a magnetic field.
  1. 1

    Enough for 1 mark

    Magnetic flux through a surface is the measure of the magnetic field passing normally through that surface. For a uniform magnetic field, it is given by PhiB = B A cos θ.

  2. 2

    Add for 2 marks

    Example: If a coil is kept with its plane perpendicular to a magnetic field, its area vector is parallel to the field, so θ = 0 degrees and flux is maximum: PhiB = BA.

  3. 3

    Add for 3 marks

    Magnetic flux depends on three things: magnetic field strength B, area A, and the angle θ between the magnetic field and the area vector.

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