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Chapter 30: Q98P (page 902)

The inductance of a closely wound coil is such that an emf of 3.00mVis induced when the current changes at the rate of 5.00A/s. A steady current of 8.00Aproduces a magnetic 铿倁x of 40.0 mWbthrough each turn. (a) Calculate the inductance of the coil. (b) How many turns does the coil have?

Short Answer

Expert verified
  1. The inductance of the coil isL=6脳10-4H
  2. The number of turns of the coil isN=120

Step by step solution

01

Given

蔚=3.00mV=0.003Vdidt=5.00A/si=8.00A蠒B=40.0渭奥产

02

Understanding the concept

By using the equation 30-35 we can find the inductance of the coil.If we pass a current iin the turns of the solenoid we can consider it as an inductor, the current produces a magnetic flux蠒Bthrough the central region of the inductor. The inductance of the inductor is then defined interms of that flux as by equation 30-28.

Formula:

蔚=-LdidtL=N蠒Bi

03

Calculate the inductance of the coil.

By using the equation 30-35 we can find the inductance

蔚=-Ldidt

Rearrange as

L=蔚didtL=0.0035.00L=6脳10-4H

04

(b) Calculate the number of turns of the coil.

According to equation 30-28 the inductance can be defined as

L=N蠒Bi

We have to find the number of turns so the formula rearrange as

N=Li蠒B

By substituting the value we get,

N=6脳10-4脳840脳10-6N=120

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Most popular questions from this chapter

A certain elastic conducting material is stretched into a circular loop of 12.0 cm radius. It is placed with its plane perpendicular to a uniform 0.800 Tmagnetic field. When released, the radius of the loop starts to shrink at an instantaneous rate of 75.0cm/s. What emf is induced in the loop at that instant?

A solenoid having an inductance of6.30渭贬is connected in series with a 1.20k惟resistor. (a) If a 14.0Vbattery is connected across the pair, how long will it take for the current through the resistor to reach 80.0% of its final value?

(b) What is the current through the resistor at timet=1.0蟿L?

Att=0, a battery is connected to a series arrangement of a resistor and an inductor. If the inductive time constant is 37.0 ms, at what time is the rate at which energy is dissipated in the resistor equal to the rate at which energy is stored in the inductor鈥檚 magnetic field?

Question: A small circular loop of area 2.00cm2200 Ais placed in the plane of, and concentric with, a large circular loop of radius 1.00 t = 0.500 s. The current in the large loop is changed at a constant rate from -200 A to(a change in direction) in a time of 1.00 s, starting at t = 0. (a) What is the magnitude of the magnetic field Bat the center of the small loop due to the current in the large loop at t = 0?(b) What is the magnitude of the magnetic field B鈬赌at the center of the small loop due to the current in the large loop at t = 0.500 s?(c) What is the magnitude of the magnetic fieldat the center of the small loop due to the current in the large loop at t =1.00s? (d) Fromt = 0 to t = 1.00 s, isB鈬赌. reversed? Because the inner loop is small, assumeB鈬赌is uniform over its area. (e) What emf is induced in the small loop at ?

Figure 30-24 shows two circuits in which a conducting bar is slid at the same speed vthrough the same uniform magnetic field and along a U-shaped wire. The parallel lengths of the wire are separated by 2Lin circuit 1 and by Lin circuit 2. The current induced in circuit 1 is counter clockwise. (a) Is the magnetic field into or out of the page? (b) Is the current induced in circuit 2 clockwise or counter clockwise? (c) Is the emf induced in circuit 1 larger than, smaller than, or the same as that in circuit 2?
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