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251.	A coil of 200 turns carries a current of 4 A. If the magnetic flux through the coil is 6 x 10-5 Wb, find the magnetic energy stored in the medium surrounding the coil.
Answer» Number of turns of the coil, N = 200 Current, I = 4 A Magnetic flux through the coil, Φ = 6 x 10^-5 Wb Energy stored in the coil, U = \(\frac{1}{2}\) LI²= \(\frac{1}{I^2}\) Self inductance of the coil, L = \(\frac{NΦ}{I}\) U = \(\frac{1}{2} \frac{NΦ}{I}\) x I² = \(\frac{1}{2} \frac{NΦ}{I}\) = \(\frac{1}{2}\) x 200 x 6 x 10^-5 x 4 U = 2400 x 10^-5= 0.024 J (or) joules.

251.

A coil of 200 turns carries a current of 4 A. If the magnetic flux through the coil is 6 x 10-5 Wb, find the magnetic energy stored in the medium surrounding the coil.

Answer»

Number of turns of the coil, N = 200

Current, I = 4 A

Magnetic flux through the coil, Φ = 6 x 10^-5 Wb

Energy stored in the coil, U = \(\frac{1}{2}\) LI²= \(\frac{1}{I^2}\)

Self inductance of the coil, L = \(\frac{NΦ}{I}\)

U = \(\frac{1}{2} \frac{NΦ}{I}\) x I² = \(\frac{1}{2} \frac{NΦ}{I}\) = \(\frac{1}{2}\) x 200 x 6 x 10^-5 x 4

U = 2400 x 10^-5= 0.024 J (or) joules.

Discussion

252.	A straight metal wire crosses a magnetic field of flux 4 mWb in a time 0.4 s. Find the magnitude of the emf induced in the wire.
Answer» Magnetic flux (Φ) = 4 m Wb = 4 × 10^-3 Wb time (t) = 0.4 s The magnitude of induced emf (e) = \(\frac{dΦ}{dt}\) =\(\frac{ 4 \times 10^{-3}}{0.4}\) =10^-2 e = 10 mV

252.

A straight metal wire crosses a magnetic field of flux 4 mWb in a time 0.4 s. Find the magnitude of the emf induced in the wire.

Answer»

Magnetic flux (Φ) = 4 m Wb = 4 × 10^-3 Wb time (t) = 0.4 s

The magnitude of induced emf (e) = \(\frac{dΦ}{dt}\) =\(\frac{ 4 \times 10^{-3}}{0.4}\) =10^-2

e = 10 mV

Discussion

253.	A square coil of side 30 cm with 500 turns is kept in a uniform magnetic field of 0.4 T. The plane of the coil is inclined at an angle of 30° to the field. Calculate the magnetic flux through the coil.
Answer» Square coil of side (a) = 30 cm = 30 × 10^-2 m Area of square coil (A) = a² = (30 × 10^-2 )2 = 9 × 10^-² m² Number of turns (N) = 500 Magnetic field (B) = 0.4 T Angular between the field and coil (θ) = 90 – 30 = 60° Magnetic flux (Φ) = NBA cos 0 = 500 × 0.4 × 9 × 10^-2 × cos 60° = 18 ×\(\frac{1}{2}\) Φ = 9 W b

253.

A square coil of side 30 cm with 500 turns is kept in a uniform magnetic field of 0.4 T. The plane of the coil is inclined at an angle of 30° to the field. Calculate the magnetic flux through the coil.

Answer»

Square coil of side (a) = 30 cm = 30 × 10^-2 m

Area of square coil (A) = a² = (30 × 10^-2 )2 = 9 × 10^-² m²

Number of turns (N) = 500

Magnetic field (B) = 0.4 T

Angular between the field and coil (θ) = 90 – 30 = 60°

Magnetic flux (Φ) = NBA cos 0 = 500 × 0.4 × 9 × 10^-2 × cos 60° = 18 ×\(\frac{1}{2}\)

Φ = 9 W b

Discussion

254.	Why does a metallic piece become very hot when it is surrounded by a coil carrying high frequency alternating current?
Answer» Due to flow of high frequency alternating current in the coil, the magnetic flux linked with the metallic piece changes by a large amount, so heavy eddy currents are induced in the metallic piece. These currents cause metallic piece to get heated.

Discussion

255.	Consider a magnet surrounded by a wire with an on/off switch S (as shown in figure). If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain.
Answer» No part of the wire is moving and so motional emf is zero. The magnet is stationary and hence the magnetic field does not change with time. This means no electromotive force is produced and hence no current will flow in the circuit.

Discussion

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Explore topic-wise InterviewSolutions in .

A coil of 200 turns carries a current of 4 A. If the magnetic flux through the coil is 6 x 10-5 Wb, find the magnetic energy stored in the medium surrounding the coil.

A straight metal wire crosses a magnetic field of flux 4 mWb in a time 0.4 s. Find the magnitude of the emf induced in the wire.

A square coil of side 30 cm with 500 turns is kept in a uniform magnetic field of 0.4 T. The plane of the coil is inclined at an angle of 30° to the field. Calculate the magnetic flux through the coil.

Why does a metallic piece become very hot when it is surrounded by a coil carrying high frequency alternating current?

Consider a magnet surrounded by a wire with an on/off switch S (as shown in figure). If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain.