An experiment is carried out using a small circular probe coil placed at the center of a Helmholtz coil pair connected to a sinusoidal alternating current supply. The plane of the probe coil is oriented such that the normal to its face makes an angle ϕ\phiϕ with the central axis of the Helmholtz coils.
The maximum alternating induced electromotive force (e.m.f.) across the ends of the probe coil is VmaxV_{\max}Vmax.
Name an instrument that can be used to determine VmaxV_{\max}Vmax.
The equation for VmaxV_{\max}Vmax is:
Vmax=ΓI0ANfcosϕV_{\max} = \Gamma I_0 A N f \cos \phiVmax=ΓI0ANfcosϕ
where:
- I0I_0I0 is the peak current in the Helmholtz coils
- AAA is the cross-sectional area of the probe coil
- NNN is the number of turns of the probe coil
- fff is the frequency of the alternating current
- Γ=3.6×10−3 V A−1 m−2 s\Gamma = 3.6 \times 10^{-3} \text{ V A}^{-1} \text{ m}^{-2} \text{ s}Γ=3.6×10−3 V A−1 m−2 s
The magnitude of the induced e.m.f. can be determined using Faraday's law of electromagnetic induction:
e.m.f.=rate of change of magnetic flux linkage\text{e.m.f.} = \text{rate of change of magnetic flux linkage}e.m.f.=rate of change of magnetic flux linkage
Suggest which quantity, or quantities, in the equation for VmaxV_{\max}Vmax are linked to:
- the 'rate' part of the law
- the 'change of magnetic flux linkage' part of the law
A student plots a straight-line graph of VmaxV_{\max}Vmax against cosϕ\cos \phicosϕ.
Determine the frequency fff, including its absolute uncertainty. Write your value of fff to 2 significant figures.
Given data:
- I0=(4.8±0.2) AI_0 = (4.8 \pm 0.2) \text{ A}I0=(4.8±0.2) A
- A=(7.2±0.1)×10−5 m2A = (7.2 \pm 0.1) \times 10^{-5} \text{ m}^2A=(7.2±0.1)×10−5 m2
- N=3500N = 3500N=3500
- gradient of line=ΓI0ANf=(0.28±0.01) V\text{gradient of line} = \Gamma I_0 A N f = (0.28 \pm 0.01) \text{ V}gradient of line=ΓI0ANf=(0.28±0.01) V