Question

A solenoid with 2000 turns/meter is connected to a power source that delivers an increasing current i60t^2 Ampere.The solenoid has a length of 0.2 m and a radius of 0.05 m.

a.what is the magnetic field as a function of timr inside the solenoid?

b.Use Faraday's law to find the induced emf caused by this changing magnetic field.

Answer 1

Number of turns per meter of solenoid n = 2000 turns/m

Current in solenoid i = 60t² A

Length of solenoid L = 0.2 m

Radius of the solenoid r = 0.05 m

a) Magnetic field inside solenoid is given by

.........................................................1)

where n = number of turns per unit length

  

  

Differentiating above equation with respect to t we get

  

  

,,,,, ...........................................................2)

b) Fardaday's law for changing magnetic field is given by

where = magnetic flux

= nL = (2000x0.2) = 400 turns

A = r² = (0.05)² = Cross section area

using value from equation 2 we get

(Since L = 0.2m , it has two significant digits, thus induce e.m.f in two significant digits)

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