The figure below shows a compact, circular coil with 258 turns and radius 12.0 c

Question

The figure below shows a compact, circular coil with 258 turns and radius 12.0 cm immersed in a uniform magnetic field parallel to the axis of the coil. The rate of change of the field has the constant magnitude 22.5 mT/s.

(a) What additional information is necessary to determine whether the coil is carrying clockwise or counterclockwise current?

This answer has not been graded yet.

(b) The coil overheats if more than 177 W of power is delivered to it. What resistance would the coil have at this critical point?
??

(c) To run cooler, should it have lower resistance or higher resistance?

lower resistancehigher resistance   

The figure below shows a compact, circular coil with 258 turns and radius 12.0 cm immersed in a uniform magnetic field parallel to the axis of the coil. The rate of change of the field has the constant magnitude 22.5 mT/s. (a) What additional information is necessary to determine whether the coil is carrying clockwise or counterclockwise current? This answer has not been graded yet. (b) The coil overheats if more than 177 W of power is delivered to it. What resistance would the coil have at this critical point? ?? (c) To run cooler, should it have lower resistance or higher resistance? lower resistancehigher resistance

Explanation / Answer

a)

The sign of the rate of change needs to be given to ascertain the direction of current

That is if the magnetic field is increasing or decreasing needs to be given

b)

Induced emf , E = N*A*dB/dt

where N = 258

r = 12 cm = 0.12 m

A = pi*r^2 = pi*0.12^2

dB/dt = 22.5 mT/s = 0.0225 T/s

So, E = 258*pi*0.12^2*0.0225 = 0.263 V

Now let the resistance be R

So, heat dissipation power , P = E^2/R = 177

So, R = 0.263^2/177 = 3.9*10^-4 ohm <------------answer

c)

To run cooler it must have higher resistance as H is inversely proportional to R

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