MUST ANSWER ALL 3 PARTS CORRECTLY WITH DETAILED EXPLANATION TO GET 5 STARS Probl

Question

MUST ANSWER ALL 3 PARTS CORRECTLY WITH DETAILED EXPLANATION TO GET 5 STARS

Problem 25.63 A 18-cm-long, zero-resistance wire is pulled outward, on zero-resistance rails, at a steady speed of 1.0m/s in a 0.10 T magnetic field (See the figure). On the opposite side. a 1.0 omega carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 66mg .(Figure 1) Part A What s the induced current in the circuit? Part B How much force is needed to pull the wire at this speed? Part C How much does the temperature of the carbon increase if the wire is pulled for 10 s? The specific heat of carbon is 710 J/kg. degree C.

Explanation / Answer

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = lvB

where l is length

v is speed

B is magnetic field

so
so induced emf e =   0.18 * 1 *0.1

emf e 0.018 Volts

now induced current i = e/R

Where R = resisatnce

so i = 0.018/1 = 0.018 Amps or 18 mA

-----------------------------

apply mangetic force F = iLB

wnhere i is current

L is length

B is magnetic field

so

F = 0.018 * 0.18 * 0.1

F = 3.24 *10^-4 N

-------------------------

apply enenrgy E = vit * mcDT

where v is emf, i is current

t is time

m is mass

c is Sp heat of Copper   = 387

DT is the change of temperature = ?

so

DT = Vit/mc

DT = 0.018 *0.018 * 10/(0.066 * 387)

DT = 0.000126 deg C

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