Question

When a magnetic field is first turned on, the flux through a 20-turn loop varies with time according to Φm=5.0t2−2.0t, where Φm is in milliwebers, t is in seconds, and the loop is in the plane of the page with the unit normal pointing outward. (a) What is the emf induced in the loop as a function of time? What is the direction of the induced current at (b) t = 0, (c) 0.10, (d) 1.0, and (e) 2.0 s?

Answer 1

A) ( - 200t + 40 ) volts

B) b) anticlockwise , c) anticlockwise , d) clockwise , e) clockwise

Step-by-step explanation:

Given data:

magnetic flux (Φm) = 5.0t^2 − 2.0t

number of turns = 20

a) determine induced emf

E = - N
`(d\beta )/(dt)`

= - N ( 10t - 2 ) = - 20 ( 10t - 2 )

= - 200t + 40 volts

b) Determine direction of induced current

i) at t = 0

E = - 0 + 40 ( anticlockwise direction )

ii) at t = 0.10

E = -20 + 40 = 20 ( anticlockwise direction )

iii) at t = 1

E = - 200 + 40 = - 160 ( clockwise direction)

iv) at t = 2

E = -400 + 40 = - 360 ( clockwise direction )