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Numerical Methods

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Question 58

A physicist is measuring the net magnetic flux density B B\,B inside a custom solenoid as the control current I I\,I is adjusted. The physicist correctly establishes that

B(−5)<0 and B(5)>0 B(-5) < 0 \text{ and } B(5) > 0 B(−5)<0 and B(5)>0

and concludes that there must be an equilibrium current level in the interval I∈(−5,5)I \in (-5, 5)I∈(−5,5) where the flux density is exactly zero (B=0B = 0B=0), citing the change of sign. For which of the following models for B(I)B(I)B(I) is this conclusion incorrect? Explain your answer.

  • B(I)=0.4IB(I) = 0.4IB(I)=0.4I
  • B(I)=10I\displaystyle B(I) = \frac{10}{I}B(I)=I10​
  • B(I)=0.016I3B(I) = 0.016I^3B(I)=0.016I3
  • B(I)=6II+10\displaystyle B(I) = \frac{6I}{I+10}B(I)=I+106I​
[3]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Maths
  3. /Numerical Methods

321 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

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