Question

okay so i am working on a physic review quetion that i seem not to know where to start..

It states as follow

A magnetic field of .250T points straight up in a lab, a circular coil of wire with 10 turns, a radius of 12 cm and a resistance of 1.6 ohms, sits on a slanted surface, tilted at 30 degress from horizontal. Then the magnetic field is turn off and it decays exponentially to 0. (B=B_oe^-t/T) At the time B reaches .125 T, the indued current in the coil is 100 uA.

then the questions ask

what is the emf induced at this time

what is the rate at which the flux is changing at this time

what is the rate at which B is changing at this time

how long has B been decreasing at this time?

what is T

what is the max induced current, and when did it flow

how much energy is dissipated in the coil, total?

and what time has 90% of the energy been dissipated?

Answer 1

Given Data

magnetic field B0 = 0.250T

No of turns, n = 10 turns,

radius r = 12 cm = 0.12 m

resistance , R = 1.6 ohms,

Angle = 30 degress

B = 0.125 T,

indued current I = 100 uA = 100*10^-6

Solution :-

magnetic flux = N*B*A*cos30

flux = N*B*(pi*r^2)*cos30

emf induced = - rate of change in flux

emf E = -N*pi*r^2*cos30*(dB/dt)

current I = E/R

a) E = I*R

       = (100*10^-6)*1.6

E = 1.6*10^-4 V = 0.00016 V

(b) EMF = rate of change in flux

rate of change in flux = 0.00016 T m^2/s

(c) EMF = -N*pi*r^2*cos30*(dB/dt)

dB/dt = -0.00016/(N*pi*r^2*cos30)

dB/dt = -0.00016 / [10*(pi*0.12^2)*cos30)

        = -0.000408 T/s

(d)
(B - B0)/t = -0.000408

(0.125 - 0.25)/t = -0.000408

t = 306.4 s

(e) B = B0*e^-(t/T)

0.125 = 0.25*e^-(306.4/T)

0.5 = e^-(306.4/T)

ln (0.5) = (-306.4/T)

T = 442.042 s

(f) B is max dB/dt = 0

(1/T)*B0*e^-(t/T) = 0

e^-(t/442.042) = 0

Imax = Emax/R = N*pi*r^2*cos30*B0

g) Energy Dissipated, P = I^2*R

                                  = (100*10^-6)^2 * 1.6

                                 = 1.6*10^-8 W