Question

PartA A 40-cm-diameter loop with resistance 0.19 Ω around a 2.0-cm-diameter solenoid. The solenoid is 14 cm long, has 100 turns, and carries the current shown in the graph. A positive current is cw when seen from the left. Figure 1) Find the current in the loop at t 0.5s. Express your answer as an integer and include the appropriate units. I(0.5)-Value Units Submit Figure 1 of 1 Part B Find the current in the loop at t-1.5s. Express your answer to two significant figures and include the appropriate units. 20 4.0 cm 2.0 cm r (s) 1 2 3 20 (1.5)Value Units Submit uest Answer

C) Find the current in the loop at t = 2.5s.

Express your answer as an integer and include the appropriate units.

Answer 1

A] The current in the solenoid is not changing at t = 0.5s and so the magnetic field is constant at this time. This implies that the magnetic flux is constant. From Faraday's law of electromagnetic induction, an emf (hence a current) will be induced whenever there is a change in magnetic flux with time. Therefore, the current at t = 0.5s is I = 0 A.

B]

The emf induced in the coil is given by:

$|\varepsilon| = \mu_o [N/L]A\left(\frac{20-(-20)}{2-1} \right ) = 40\mu_o (N/L)A$ = 0.1804 mV

from Ohm's law, the induced current at t = 1.5s is then,

i = V/R = 0.95 mA

C] At t = 2.5s, the current in the solenoid again becomes constant thereby making the magnetic flux constant. So, the emf induced is zero and therefore the current in coil is zero.