Answer:
[tex]1.138\times 10^{-3}V[/tex]
Explanation:
Apply Faraday's Newmann Lenz law to determine the induced emf in the loop:
[tex]\epsilon=\frac{d\phi}{dt}[/tex]
where:
[tex]d\Phi-[/tex]variation of the magnetic flux
[tex]dt-[/tex]is the variation of time
#The magnetic flux through the coil is expressed as:
[tex]\Phi=NBA \ Cos \theta[/tex]
Where:
N- number of circular loops
A-is the Area of each loop([tex]A=\pi r^2=\pi \times 5^2=78.5398[/tex])
B-is the magnetic strength of the field.
[tex]\theta=15\textdegree[/tex]- is the angle between the direction of the magnetic field and the normal to the area of the coil.
[tex]\epsilon=-\frac{d(78.5398\times 10^{-3}NB \ Cos \theta)}{dt}\\\\=-(78.5398\times 10^{-3}N\ Cos \theta)}{\frac{dB}{dt}[/tex]
[tex]\frac{dB}{dt}-[/tex]=0.0250T/s is given as rate at which the magnetic field increases.
#Substitute in the emf equation:
[tex]=-(78.5398\times 10^{-3} m^2 \times 6\ Cos 15 \textdegree)\times 0.0250T/s\\\\=1.138\times 10^{-3}V[/tex]
Hence, the induced emf is [tex]1.138\times 10^{-3}V[/tex]
