Mutual Induction of a solenoid and a coil

In summary, the conversation discusses the calculation of induced emf in a circular loop due to a changing current in a solenoid. The relevant equations and attempt at a solution are also mentioned. The speaker is seeking help in finding the correct answer.
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shuangfei217
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Homework Statement



A single-turn circular loop of radius R = 0.235 m is coaxial with a long 1780 turn solenoid of radius 0.0435 m and length 0.850 m, as seen in the figure below. The variable resistor is changed so that the solenoid current decreases linearly from 6.12 A to 1.46 A in 0.230 s. Calculate the induced emf in the circular loop. (The field just outside the solenoid is small enough to be negligible.)

Homework Equations



M=N*∏*μ0*n*r^2

Vind = - N*∏*μ0*n*r^2 * di/dt

di/dt=(1.46-6.12)/0.23

The Attempt at a Solution



I used mutual inductance equ to find the potential difference induced

N is 1780, n=N/length, r=0.0435

but I still can't get the correct answer. I don't know where I did wrong here. Does anybody help me to find the answer? Thank you
 

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Does anyone can help me?
 

Related to Mutual Induction of a solenoid and a coil

What is mutual induction?

Mutual induction is the process by which a changing magnetic field in one circuit induces a voltage in a nearby circuit.

What is a solenoid?

A solenoid is a coil of wire that produces a magnetic field when an electric current passes through it.

What is a coil?

A coil is a series of loops or windings of wire that can carry an electric current and produce a magnetic field.

How does mutual induction occur between a solenoid and a coil?

Mutual induction between a solenoid and a coil occurs when the changing magnetic field produced by the solenoid induces a current in the coil. This is because the changing magnetic field creates an electric field in the coil, which in turn causes a current to flow.

What are some real-world applications of mutual induction between a solenoid and a coil?

Mutual induction between a solenoid and a coil is used in various devices, such as transformers, electric motors, and generators. It is also used in wireless charging systems and inductive power transfer systems.

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