A circular coil of 20 turns and radius 5.0 cm is placed with its plane oriented at 90° to a uniform magnetic field of 0.1 T. The field is now increased at a steady rate, reaching a value of after 4.0 seconds. What emf is induced in the coil?
Answers
Answer:
A circular coil of 20 turns and radius 5 cm is placed with its plane oriented at 90 degrees to a magnetic field of 0.1 T. The field is now increased at a steady rate, ...
Explanation:
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The emf induced in the coil is 0.016V
Given:
n = 20
r = 5cm
Θ = 0° (the plane and magnetic field flux are parallel as the plane is oriented at 90 degrees to a uniform magnetic field)
B₁ = 0.1T
B₂ = 0.5T
t = 4s
To Find :
The emf induced in the coil
Solution:
The cross-sectional area of the loop can be found by
A = π . r²
= 3.14 x (0.05)²
= 78.539 x 10⁻⁴m²
The initial magnetic flux ∅₁ is given by
∅₁ = B₁Acosθ
= 0.1 x 78.539 x 10⁻⁴ x cos 0°
= 7.8539 x 10⁻⁴Tm²
The final magnetic flux ∅₂ is given by
∅₂ = B₂Acosθ
= 0.5 x 78.539 x 10⁻⁴ x cos 0°
= 39.2695 x 10⁻⁴ Tm²
The induced emf is computed by,
emf = N(∅₂ - ∅₁)/Δt
= 20(39.2695 * 10⁻⁴- 7.8539 * 10⁻⁴)/4.0
= 0.0157V
emf ≈ 0.016V
Therefore, the induced emf in the coil is 0.016V
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