This question is incomplete, the complete question is;
A 70-turn coil has a diameter of 11 cm. Find the magnitude of the emf induced in the coil (in V) if it is placed in a spatially uniform magnetic field of magnitude 0.70 T so that the face of the coil makes the following angles with the magnetic field, and the magnetic field is reduced to zero uniformly in 0.2 s. a) θ = 30° V b) θ = 60° V c) θ = 90° V
Answer:
the magnitude of the emf induced in the coil are;
a)- For θ = 30°, e = 1.16 V
b)- For θ = 60°, e = 2.01 V
c)- For θ = 90°, e = 2.33 V
Step-by-step explanation:
Given the data in the question;
number of turns N = 70
Diameter of coil D = 11 cm
Radius r = D/2 = 11/2 = 5.5 cm = 0.055 m
magnitude of magnetic ΔB = 0.7T
Δt = 0.2 seconds
Now,
a)
For θ = 30°,
Angle of with area of vector θ' = 90° - 30° = 60°
so
emf e = N( Δ∅ / Δt ) = N( ΔBAcosθ / Δt )
hence
e = NAcosθ'(ΔB / Δt )
where A is area ( πr² )
so we substitute
e = 70 × πr² × cos(60°) × ( 0.7 / 0.2 )
e = 70 × π(0.055)² × cos(60°) × ( 0.7 / 0.2 )
e = 1.16 V
b)
For θ = 60°,
Angle of with area of vector θ' = 90° - 60° = 30°
so
e = NAcosθ'(ΔB / Δt )
we substitute
e = 70 × πr² × cos(30°) × ( 0.7 / 0.2 )
e = 70 × π(0.055)² × cos(30°) × ( 0.7 / 0.2 )
e = 2.01 V
c)
For θ = 90°,
Angle of with area of vector θ' = 90° - 90° = 0°
so
e = NAcosθ'(ΔB / Δt )
we substitute
e = 70 × πr² × cos(0°) × ( 0.7 / 0.2 )
e = 70 × π(0.055)² × cos(30°) × ( 0.7 / 0.2 )
e = 2.33 V
Therefore, the magnitude of the emf induced in the coil are;
a)- For θ = 30°, e = 1.16 V
b)- For θ = 60°, e = 2.01 V
c)- For θ = 90°, e = 2.33 V