Question

3) In the figure below, the magnetic flux through the loop shown increases according to the equation, \(\Phi=8 t^{3}-3 t^{2}\) where \(\Phi\) is in webers and \(t\) is in seconds:

a) What is the induced voltage across the resistor at \(t=2\) seconds? 

b) What is the polarity of the voltage across the resistor

c) If the area of the entire closed loop is \(14 \mathrm{~m}^{2}\), what is the magnitude of the magnetic field at \(t=2\) seconds? 

Answer 1

a)
Magnetic flux,
_{3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t}
= 8 * t³ - 2 * t²
Induced EMF, E(t) = d
_{3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t}
/dt
= d/dt [8 * t³ - 2 * t²]
= 24 * t² - 4 * t

EMF at t = 2 s,
E = 24 * 2² - 4 * 2
= 88 V
--------------------------------------
b)
The magnetic flux is increasing through the area of the loop in the out of the page direction. So the induced magnetic field must be into the page. For this, the current must be clockwise. The current through the resistor is towards left, which is same as the direction of the polarity of voltage, from right to left.

c)

_{3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t}
= B * A
B =
_{3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t}
/A

_{3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t}
= 8 * t³ - 2 * t²
At t = 2 s,

_{3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t}
= 8 * 2³ - 2 * 2² = 56 Wb
A = 14 m²

B = 56 / 14
= 4 T

Answer 2

3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t

Answer 3

3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t

Answer 4

3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t

et t = 28. lel 24x4 - 6x2=940 le) - 84u eincreasing According to As the flume Q is end » B es also eincreasing is out of the page' Lena's low the induced current is such that, et opposes the change has induced et. Therefore current is the loop must be in the direction corresponching to that they feeld opposes the inducing field. induced Keepeng in mind the above fact, induced current marf flow clockwise ein loop and therefore the ER is havery are at skert and are at regul + VR 3(c) A=14m2 At + =25, d = szweb af at t=21. 0 Ba 3.71T B: 3.71

Answer 5

3Ca) We have 여 그883 342 ㅋ 24t르 6t G 1월 dh 246t

et t = 28. lel 24x4 - 6x2=940 le) - 84u eincreasing According to As the flume Q is end » B es also eincreasing is out of the page' Lena's low the induced current is such that, et opposes the change has induced et. Therefore current is the loop must be in the direction corresponching to that they feeld opposes the inducing field. induced Keepeng in mind the above fact, induced current marf flow clockwise ein loop and therefore the ER is havery are at skert and are at regul + VR 3(c) A=14m2 At + =25, d = szweb af at t=21. 0 Ba 3.71T B: 3.71