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ID: 3897673 • Letter: #

Question

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Explanation / Answer

Firstly, the quantity which is measured in Teslas, and symbolised by B is magnetic flux density. Magnetic field strength is a completely different quantity and concept. It is symbolised by H and measured in units of amps/metre. If you are going to get anywhere in this topic it is essential that you distinguish between these two quantities and use the appropriate language.

The voltage that is induced in a single loop by a changing flux density is equal to the rate of change of flux (dF/dt) linking the loop. If B is uniform over the area (A) of the loop, and the plane of the loop is normal to the direction of the B vector, then dF/dt is equal to A*dB/dt, and the voltage is A*dB/dt. This is the maximum voltage that can be induced; at all other orientations of the loop with respect to B, the voltage will be less.

In your example, assuming that by 'magnetic field' you mean 'magnetic flux density', you can write -

B = 10-3 *sin(w*t) where w = 2*pi*60 rad/s. .. (1)

Now B, and therefore F vary with time, so we seek another maximum.

Differentiate (1) to get -

dB/dt = (10^-3)*w*cos(w*t)

The maximum value of dB/dt is therefore 2*pi*60*10^-3; this occurs when cos(wt) = 1

The maximum induced voltage (V) is then the product of this value of dB/dt with the area of the blood cell (A).

A = pi*(4*10^-6)^2

V = (2*pi*60*10^-3)*pi*(4*10^-6)^2 = 18.930*10^-12V