Complete Question
An emf is induced in a conducting loop of wire 1.12m long as its shape is.
changed from square to circular. Find the average magnitude of the induced emf if the change in shape occurs in 0.125 ss and the local 0.504-TT magnetic field is perpendicular to the plane of the loop.
Answer:
The induced emf is [tex]\epsilon = 0.0863 \ V[/tex]
Explanation:
From the question we are told that
The time taken is [tex]\Delta t = 0.125 \ s[/tex]
The magnitude of the magnetic field is B = 0.504 T
The length of the loop wire is [tex]l = 1.12 \ m[/tex]
Generally the circumference of the wire when in circular form is
[tex]C = 2 \pi r[/tex]
=> [tex]l = 2 \pi r[/tex]
=> [tex]r =[/tex][tex]\frac{l}{2 \pi}[/tex]
=> [tex]r =[/tex][tex]\frac{1.12}{2 * 3.142}[/tex]
=> [tex]r =[/tex][tex]0.1782 \ m[/tex]
Now the area of the wire as a circle is
[tex]A = \pi r^2[/tex]
=> [tex]A = 3.142 * (0.1782)^2[/tex]
=> [tex]A = 0.0998 \ m^2[/tex]
The length of one side of the square is
[tex]b = \frac{l}{4}[/tex]
[tex]b = \frac{1.12}{4}[/tex]
[tex]b = 0.28 \ m[/tex]
Now the area of the wire as a square is
[tex]A_s = b^2[/tex]
=> [tex]A_s =(0.28 )^2[/tex]
[tex]A_s = 0.0784 \ m^2[/tex]
Generally the induced emf is mathematically represented as
[tex]\epsilon = \frac{B * [A - A_s ]}{\Delta t }[/tex]
=> [tex]\epsilon = \frac{0.504 * [0.0998 - 0.0784 ]}{0.125 }[/tex]
=> [tex]\epsilon = 0.0863 \ V[/tex]
