Question

A coil of wire enclosing an area 100 cm2 is placed with its plane making an
angle 60° with the magnetic field of strength 10-1T. What is the flux through
the coil? If magnetic field is reduced to zero in 10 s, then find the induced
emf?
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Answer 1

Given:

• Area(A) = $100cm^{2} = 100*10^{-4} m$
• Angle(θ) = 60°
• Magnetic Field(B) = $10^{-1} T$  

To Find:

• The flux through the coil
• Induced EMF when the magnetic field is reduced to zero in 10s.

Solution:

• The formula to find flux is given as, φ = BA cosθ
• Where, B is the magnetic field and A is the area of the coil.
• Substituting then given values in the formula we get.
• φ = $10^{-1} *100*10^{-4} *cos(60)$ = $100*10^{-5} *\frac{1}{2}$
• φ = $50*10^{-5} = 5*10^{-4}wb$
• now we have to find the induced emf when the magnetic field is reduced to zero.
• The formula for induced emf is   E = -dφ/dt
• dt is given as 10 s and dφ = φ(f)-φ(i)
• Here φ(f) = 0
• So, $E = \frac{-(0-5*10^{-4})}{10}$ = $\frac{5*10^{-4} }{10}$ = $\frac{1}{2}*10^{-4}$ = $0.5*10^{-4} v$

The flux through the coil is $50*10^{-5} = 5*10^{-4}wb$

The Induced EMF at t = 10s is $0.5*10^{-4} v$