6.5.5 Magnetic Flux Density

Aims of the Experiment

• The overall aim of this experiment is to calculate the magnetic flux density of a magnet
  • This is done by measuring the force on a current-carrying wire placed perpendicular to the field

Variables

• Independent variable = Current, I
• Dependent variable = mass, m
• Control variables:
  • Length of wire, L
  • Magnetic Flux density, B
  • Potential difference of the power supply

Equipment List

• Resolution of measuring equipment:
  • Ammeter = 0.01 A
  • Variable resistor = 0.01 Ω
  • Top-pan balance = 0.01 g
  • Ruler = 1 mm

Method

1. Set up the apparatus as shown above
   • Make sure the wire is completely perpendicular in between the magnets
2. Measure the length of one of the magnets using the 30 cm ruler
   • This will be the length of the wire L in the magnetic field
3. Once the magnet is placed on the top-pan balance, and whilst there is no current in the wire, reset the top-pan balance to 0 g
4. Adjust the resistance of the variable resistor so that a current of 0.5 A flows through the wire as measured on the ammeter
5. The wire will experience a force upwards.
   • Due to Newton’s third law, the force pushing downwards will be the mass on the balance.
   • This movement will be very small, so it may not be completely visible
6. Record the mass on the top-pan balance from this current
7. Repeat the procedure by increasing the current in intervals of 0.5 A between 8−10 readings for the current (not exceeding 6 A)
8. Repeat the experiment at least 3 times, and calculate the mean of the mass readings

• An example table might look like this:

Analysing the Results

• The magnetic force on the wire is:

F = BIL

• Where:
  • F = magnetic force (N)
  • B = magnetic flux density (T)
  • I = current (A)
  • L = length of the wire (m)

• Since F = mg where m is the mass in kilograms, equating these gives:

mg = BIL

• Rearranging for m:

• Comparing this to the straight-line equation: y = mx + c
  • y = m (mass)
  • x = I
  • m = BL / g
  • c = 0
• Plot a graph of m against I and draw a line of best fit
  • Calculate the gradient
• The magnetic flux density B is:

Evaluating the Experiment

Systematic Errors:

• Make sure top-pan balance starts at 0 to avoid a zero error

Random Errors:

• Repeat the experiment by turning the magnet in the metal cradle and the wire by 90º
• Make sure no high currents pass through the copper wire,
  • High current will lead to heating, causing the wire’s resistance to increase

Safety Considerations

• Keep water or any fluids away from the electrical equipment
• Make sure no wires or connections are damaged and contain appropriate fuses to avoid a short circuit or a fire
• High currents through the wire will cause it to heat up
  • Make sure not to touch the wire when current is flowing through it

Step 1: Complete the table

• • Add an extra column ‘Average mass m / × 10⁻³ kg and calculate this for each mass

Step 2: Plot the graph of average mass m against current I

• • Make sure the axes are properly labelled and the line of best fit is drawn with a ruler

Step 3: Calculate the gradient of the graph

• • The gradient is calculated by:

Step 4: Calculate the magnetic flux density, B