4. [2pt] Two very long solenoids have the same length, but solenoid A has 17 tim

Question

4. [2pt]
Two very long solenoids have the same length, but solenoid A has 17 times the number of turns, 1/5 the radius, and 6 times the current of solenoid B. Calculate the ratio of the magnetic field inside of A to that inside B.

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Answer:  

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7. [2pt]
The emf around the loop causes a current to flow. How large is that current? (Again, use a positive value for clockwise direction.)

Answer:  

8. [2pt]
From your previous results, what must be the electrical resistance of the loop? (The resistance of the rails is negligible compared to the resistance of the rod, so the resistance of the loop is constant.)

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Explanation / Answer

4) The radius doesn't matter, but the total current does: in this case, that means the current in the wire * the number of turns.

So B_A/B_B = 17*6 =102

5) Firstly, the quantity symbolised by B and measured in teslas (T) is magnetic flux density. Magnetic field (H) is a completely different concept, and its units are amps/metre.

If you intend to get anywhere in the topic of magnetism you must get used to using the correct terminology, symbols, units, etc, and distinguish between different concepts clearly.

I shall treat the question as though all references to ‘magnetic field’ are in fact intended to be to ‘flux density’.

Secondly, we are not told what points a & b refer to. I shall assume that they correspond to the ends of the coil so that we are being asked what voltage (V) appears across the resistor.

According to Faraday's law of electromagnetic induction, V = n*A* dB/dt.

Note that this applies only when B is uniform across the area (A) of the coil, and I will assume that this is intended to be the case in this question.

An additional requirement is that B should be normal to the plane of the coil, and we are told that this is so. n is the number of turns and dB/dt is the rate of change of flux density with respect to time.

V = 0.25*1000*pi*0.031^2 = 0.755V

6) E=BLv =0.6 * 0.36 * 4 = 0.864 V

7) i=F/LB= 4.90/(0.36 * 0.6) =22.685 A

8) R=E/i= 0.864/22.685 =0.038 ohms

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