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Lesson_4.3_Homework_and_Solutions

# Lesson_4.3_Homework_and_Solutions - Lesson 4.3 Homework...

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Lesson 4.3 Homework Solutions 1. A circular coil has 25 turns and a radius of 5 cm. It is at the equator where the earth’s magnetic field is 0.7 G north. Find the magnetic flux through the coil when its plane is (i) horizontal, (ii) vertical with the axis pointing north, (iii) vertical with its axis pointing east and (iv) vertical with its axis making an angle 30 o with north. (i) At the equator the earth’s field is horizontal and the angle made by the normal to the plane of the coil with the field θ = 90 o . The flux through the coil is φ B = N B A cos θ = 25 × 7.0 × 10 -5 × π × 0.05 2 × cos 90 o = 0 Wb (ii) When the coil is vertical with its axis facing north, the angle made by the normal to the plane of the coil with the field θ = 90 o . The flux through the coil is φ B = N B A cos θ = 25 × 7.0 × 10 -5 × π × 0.05 2 × cos 90 o = 0 Wb (iii) When the coil is vertical with its axis facing east, the angle made by the normal to the plane of the coil with the field θ = 0 o . The flux through the coil is φ B = N B A cos θ = 25 × 7.0 × 10 -5 × π × 0.05 2 × cos 0 o = 1.37 × 10 -5 Wb (iv) When the coil is vertical and its axis makes an angle 30 o with the north, the angle made by the normal to the plane of the coil with the field θ = 60 o . The flux through the coil is φ B = N B A cos θ = 25 × 7.0 × 10 -5 × π × 0.05 2 × cos 60 o = 6.87 × 10 -6 Wb 2. A magnetic field of 1.2 T is perpendicular to a square coil of 14 turns. The length of each side of the coil is 15 cm. (i) Find the magnetic flux through the coil. (ii) Find the magnetic flux through the coil if the magnetic field makes an angle of 60 o with the normal to the plane of the coil. Solution B = 1.2 T, N = 14 turns, aea of the coil A = 0.15 2 = 0.0225 m 2 (i) When the plane of the coil is perpendicular to B, θ = 90 o φ B = N B A cos θ = 14 × 1.2 × 0.0225 m 2 × cos 90 o = 0.378 Wb (ii) When the magnetic field makes an angle of 60 o with the plane of the coil, θ = 60 o φ B = N B A cos θ = 14 × 1.2 × 0.0225 m 2 × cos 60 o = 0.189 Wb

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3. A circular coil of radius 3.0 cm has its plane perpendicular to a magnetic field of 400 G.
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Lesson_4.3_Homework_and_Solutions - Lesson 4.3 Homework...

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