In Fig. 2a the magnetic field is perpendicular to the cross-sectional area of a
ID: 1399119 • Letter: I
Question
In Fig. 2a the magnetic field is perpendicular to the cross-sectional area of a single loop of wire (no initial current) and increases uniformly from 1.2 T ( i ) to 2.4 T ( i ) in 1.00 s. It has a resistance of 1.00 Ohms.
(a) Calculate the cross-sectional area if the circumference of the loop is 2.56 m.
(b) Calculate the resulting induced emf.
(c) Calculate the resulting induced current for a loop resistance of 1.00 Ohms. Can the direction of the current be determined? [Yes, No, Not enough information] (circle one) Explain your answer.
Figure 2aExplanation / Answer
Here ,
initial magnetic field , Bi = 1.2 i T
final magnetic field , Bf = 2.4 i T
time taken , t = 1 s
Reistance , R = 1 ohm
a)
Now, as circumference = 2*pi*r
2.56 = 2*pi*r
r = 0.4075 m
area = pi*r^2
area = pi*0.4075^2
area = 0.522 m^2
the cross sectional area is 0.522m^2
b)
induced emf = change in magnetic flux/time
induced emf = 0.522 * (2.4 - 1.2)/1
induced emf = 0.63 V
the induced emf in the loop is 0.63 V
c)
Now, using ohm's law
I = 0.63/1
I = 0.63 A
the induced current is 0.63 A
yes the direction can be determined ,
according to lenz's law
the current is CLOCkWISE as seen from the right of loop