Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to calculate the mutual inductance of systems involving multiple solenoids or conducting loops.

Q1:

A coil of 40 turns is wrapped around a long solenoid of cross-sectional area 7 . 5 × 1 0 − 3 m^{2}. The solenoid is 0.50 m long and has 500 turns.

What is the mutual inductance of this system?

The outer coil is replaced by a coil of 40 turns whose radius is three times that of the solenoid. What is the mutual inductance of this configuration?

Q2:

Two coils close to each other have a mutual inductance of 36 mH. If the current in one coil decays according to , where and , what is the emf induced in the second coil immediately after the current starts to decay at ?

Q3:

An emf of 9 . 7 × 1 0 − 3 V is induced in a coil while the current in a nearby coil is decreasing at a rate of 2.7 A/s. What is the mutual inductance of the two coils?

Q4:

When the current in one coil changes at a rate of 3.1 A/s, an emf of 9 . 7 × 1 0 − 3 V is induced in a second nearby coil. What is the mutual inductance of the two coils?

Q5:

A 500 turn solenoid is 0.60 m long and 5.5 cm in diameter. Inside the solenoid, a small single-turn circular coil is fixed in place with its face perpendicular to the long axis of the solenoid. What is the mutual inductance of this system?

Q6:

A solenoid of 𝑁 = 2 0 0 turns has length 𝑙 = 1 . 1 m and radius 𝑅 = 5 0 c m , and a second, smaller solenoid of 𝑁 = 1 0 0 turns has length 𝑙 = 0 . 9 0 m and radius 𝑅 = 2 5 c m . The smaller solenoid is placed completely inside the larger solenoid so that their long axes coincide. What is the mutual inductance of the two solenoids?

Q7:

A toroidal coil has a mean radius of 16 cm and a cross-sectional area of 0.25 cm^{2}; it is wound uniformly with 1 0 0 0 turns. A second toroidal coil of 750 turns is wound uniformly over the first coil. Ignoring the variation of the magnetic field within a toroid, determine the mutual inductance of the two coils.

Q8:

A centrifuge with a radius of 20.0 cm is uniformly brought to rest from a rotation rate of 1 0 0 0 0 rpm in a time of 30.0 s. A point 𝑃 is on the rim of the centrifuge and a line 𝐿 intersects both 𝑃 and the center of the centrifuge.

What is the magnitude of the total acceleration of the point 𝑃 at the instant 𝑡 = 2 9 . 0 s ?

What is the magnitude of the angle between the direction of the total acceleration of the point 𝑃 and the line 𝐿 ?

Don’t have an account? Sign Up