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Force on a Current-Carrying Conductor (OCR A Level Physics) : Revision Note

Katie M

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Katie M

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Magnetic Flux Density

  • The magnetic flux density B is defined as:

The force acting per unit current per unit length on a current-carrying conductor placed perpendicular to the magnetic field

  • Rearranging the equation for magnetic force on a wire, the magnetic flux density is defined by the equation:

B space equals space fraction numerator F over denominator I L end fraction

  • Where:

    • B = magnetic flux density (T)

    • F = magnetic force (N)

    • I = current (A)

    • L = length of the wire (m)

  • Note: this equation is only relevant when the B-field is perpendicular to the current

  • Magnetic flux density is measured in units of tesla, which is defined as:

A wire carrying a current of 1 A normal to a magnetic field of flux density of 1 T with a force per unit length of the conductor of 1 N m−1

  • To put this into perspective, the Earth's magnetic flux density is around 0.032 mT and an ordinary fridge magnet is around 5 mT

  • The magnetic flux density is sometimes referred to as the magnetic field strength

Worked Example

A 15 cm length of wire is placed vertically and at right angles to a magnetic field. When a current of 3.0 A flows in the wire vertically upwards, a force of 0.04 N acts on it to the left.

Determine the flux density of the field and its direction.

Answer:

Step 1: Write out the known quantities

  • Force on wire, F = 0.04 N

  • Current, I = 3.0 A

  • Length of wire, L = 15 cm = 15 × 10−2 m

Step 2: Write out the magnetic flux density B equation

B space equals space fraction numerator F over denominator I L end fraction

Step 3: Substitute in values

B space equals space fraction numerator 0.04 over denominator 3 cross times open parentheses 15 cross times 10 to the power of negative 2 end exponent close parentheses end fraction space equals space 0.09 space straight T

Step 4: Determine the direction of the B field

  • Using Fleming’s left-hand rule:

    • F = to the left

    • I = vertically downwards (flow of conventional current)

    • therefore, B = out of the page 

Force on a Current-Carrying Conductor

  • A current-carrying conductor produces its own magnetic field

    • An external magnetic field will therefore exert a magnetic force on it

  • A current-carrying conductor (e.g. a wire) will experience the maximum magnetic force if the current through it is perpendicular to the direction of the magnetic flux lines

    • A simple situation would be a copper rod placed within a uniform magnetic field

    • When current is passed through the copper rod, it experiences a force which makes it accelerate

Copper rod experiment, downloadable AS & A Level Physics revision notes

A copper rod moves within a magnetic field when current is passed through it

  • The force F on a conductor carrying current I in a magnetic field with flux density B is defined by the equation:

F space equals space B I L thin space sin space theta

  • Where:

    • F = magnetic force on the current-carrying conductor (N)

    • B = magnetic flux density of external magnetic field (T)

    • I = current in the conductor (A)

    • L = length of the conductor in the field (m)

    • θ = angle between the conductor and external flux lines (degrees)

  • This equation shows that the magnitude of the magnetic force F is proportional to:

    • Current I 

    • Magnetic flux density B

    • Length of conductor in the field L

    • The sine of the angle θ between the conductor and the magnetic flux lines

Force on conductor (1), downloadable AS & A Level Physics revision notes
Force on conductor (2), downloadable AS & A Level Physics revision notes

Magnitude of the force on a current carrying conductor depends on the angle of the conductor to the external B field

  • The maximum force occurs when sin space theta space equals space 1

    • This means theta space equals space 90 degree and the conductor is perpendicular to the B field

    • This equation for the magnetic force now becomes:

F space equals space B I L

  • The minimum force (0) is when sin space theta space equals space 0

    • This means theta space equals space 0 degree and the conductor is parallel to the B field

  • It is important to note that a current-carrying conductor will experience no force if the current in the conductor is parallel to the field

Worked Example

A current of 0.87 A flows in a wire of length 1.4 m placed at 30o to a magnetic field of flux density 80 mT.

Calculate the force on the wire.

Answer:

Step 1: Write down the known quantities

  • Magnetic flux density, B = 80 mT = 80 × 10−3 T

  • Current, I = 0.87 A

  • Length of wire, L = 1.4 m

  • Angle between the wire and the magnetic flux lines, θ = 30o

Step 2: Write down the equation for the magnetic force on a current-carrying conductor

F space equals space B I L thin space sin space theta

Step 3: Substitute in values and calculate

F space equals space open parentheses 80 cross times 10 to the power of negative 3 end exponent close parentheses open parentheses 0.87 close parentheses open parentheses 1.4 close parentheses thin space sin space 30 degree space equals space 0.049 space straight N

Examiner Tips and Tricks

Remember that the direction of current is the flow of positive charge (i.e. conventional current) and this is opposite to the flow of electrons.

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    Katie M

    Author: Katie M

    Expertise: Physics Content Creator

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.