# Magnetic Flux Density(OCR A Level Physics)

Author

Ashika

Expertise

## Determining 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
• 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

#### Worked example

A student investigates the relationship between the current and the mass produced from the magnetic force on a current-carrying wire. They obtain the following results:The mean length of the wire in the magnetic field was found to be 0.05 m. Calculate the magnetic flux density of the magnets from the table.

Step 1: Complete the table

• Add an extra column ‘Average mass m / × 103 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

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