Required practical: measuring B with a current balance

Magnetic Fields & Forces — AQA A-Level Physics

This experiment uses the teslaThe SI unit of magnetic flux density. One tesla is the flux density when a force of 1 N acts on a 1 m conductor carrying 1 A perpendicular to the field.'s own definition to measure flux densityMass per unit volume of a material. Measured in kg m⁻³.. You measure the apparent mass change on a balance when a currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).-carrying wire in a magnetic field feels a force.

Variables

Independent: currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). I through the wire.
Dependent: mass reading m on the top-pan balance.
Control: length of wire L, magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³.The strength of a magnetic field. The force per unit length per unit currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). on a current-carrying conductor perpendicular to the field. Measured in teslaThe SI unit of magnetic flux density. One tesla is the flux density when a force of 1 N acts on a 1 m conductor carrying 1 A perpendicular to the field. (T). B, e.m.f. of the powerThe rate of energy transfer. Measured in watts (W). supply.

Key apparatus

Electronic top-pan balance (0.01 g resolutionThe smallest change in a quantity that an instrument can detect. For example, a ruler has a resolution of 1 mm.) — measures force as apparent mass change.
Thick copper wire clamped perpendicular between two magnets in a metal cradle.
Variable resistor + ammeterAn instrument that measures current. Connected in series with the component. Has very low resistance so it doesn't affect the circuit. (0.01 A resolutionThe smallest change in a quantity that an instrument can detect. For example, a ruler has a resolution of 1 mm.) — varies and measures current.
DC powerThe rate of energy transfer. Measured in watts (W). supply.
30 cm ruler (1 mm resolutionThe smallest change in a quantity that an instrument can detect. For example, a ruler has a resolution of 1 mm.) — measures the magnet length, which equals L.
Crocodile clips to hold the wire in place.

Method

Set up the wire perpendicular between the magnets, which sit on the top-pan balance.
Measure magnet length with the ruler. This is L.
With magnets on the balance but no current, zero the balance.
Set 0.5 A through the wire. The wire feels a force upwards (F = BIL). By Newton's third lawWhen two objects interact, the forces they exert on each other are equal in magnitude, opposite in direction, and act on different objects., the magnets push down on the balance. The balance reads a positive mass.
Record the mass. Increase current in 0.5 A steps up to 5.0 A (never above 6 A).
Repeat at least 3 times and take mean mass at each current.

Analysis

The magnetic force equals the weight registered on the balance:

$$mg = BIL$$

Rearranging:

m = \frac{BL}{g} \times I

Plot mass (y) against current (x). $Gradient = BL/g. The line should pass through$ the origin.

B = \frac{g \times \text{gradient}}{L}

$B$: magnetic flux densityMass per unit volume of a material. Measured in kg m⁻³.The strength of a magnetic field. The force per unit length per unit current on a current-carrying conductor perpendicular to the field. Measured in teslaThe SI unit of magnetic flux density. One tesla is the flux density when a force of 1 N acts on a 1 m conductor carrying 1 A perpendicular to the field. (T). (T)
$g$: gravitational field strengthThe gravitational force per unit mass at a point in a gravitational fieldA region of space in which a mass experiences a gravitational force.. Measured in N kg⁻¹. (9.81 m s⁻²)
$gradient$: slope of m vs I graph (kg A⁻¹)
$L$: length of wire in the field (m)

Evaluation

Systematic errorAn error that shifts all readings by the same amount in the same direction. Cannot be reduced by repeating measurements.: zero the balance before starting (magnets on, no current).
Random errorAn error that causes readings to scatter unpredictably above and below the true value. Can be reduced by averaging repeated measurements.: repeat with the magnet and wire rotated 90° to check for directional effects.
Keep current below 6 A. High currents heat the wire, increasing resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). and affecting results.
Safety: keep water away from electrical equipment, check wires for damage, don't touch the wire while current flows.

Worked Example

A student plots mass against current for a wire of length 0.05 m in a magnetic field. The gradient of the line of best fit is 2.133 × 10⁻⁴ kg A⁻¹. Calculate the magnetic flux density.

Show Solution

List known values

Gradient: $\text{gradient} = 2.133 \times 10^{-4} \text{ kg A}^{-1}$
Wire length: $L = 0.05 \text{ m}$
$g = 9.81 \text{ m s}^{-2}$

Use the analysis equation

Gradient of $m$ vs $I$ graph = $\frac{BL}{g}$. Rearranging:

$$B = \frac{g \times \text{gradient}}{L}$$

Substitute values

$$B = \frac{9.81 \times 2.133 \times 10^{-4}}{0.05}$$

Evaluate

Numerator: $9.81 \times 2.133 \times 10^{-4} = 2.092 \times 10^{-3}$

$$B = \frac{2.092 \times 10^{-3}}{0.05} = 0.042 \text{ T (42 mT)}$$

Answer

$B = 0.042$ T (42 mT)

Examiner Tips and Tricks

The mass change is very small — fractions of a gram.
Convert grams to kilograms before calculating B.
If the line of best fit doesn't pass through the origin, you have a zero error on the balance.

Related:Magnetic Flux EM Induction