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Chapter 30: Q. 74 (page 874)

74. II The inductor in FIGURE P30.74 is a 9.0鈭�cm-long, 2.0鈭�cm鈭�diameter solenoid wrapped with 300 turns. What is the current in the circuit 10渭safter the switch is moved from a to b ?

Short Answer

Expert verified

Hence, the required current is0.093A

Step by step solution

01

Step 1. Given information

The number of turns if 300, and length of inductor is 9 cm

The radius of the coil is,

r=d2r=2cm1m100cm2=0.01m

02

Step 2. Explanation

The inductance of the coil is,

L=渭0N2AlL=渭0N2蟺r2lL=4蟺脳10鈭�7T鈰�m/A(300)2蟺(0.01m)29cm1m100cm=3.94脳10鈭�4H

According to ohm's law, the initial current is,

I0=V0RI0=6V30惟=0.2A

The expression for the current in the coil is,

I=I0e鈭�t蟿I=I0e鈭�tLR=I0e鈭�RtLI=I0e鈭�RtLI=(0.2A)e鈭�(30惟)(10渭s)10鈭�4s1/s=0.093A

Hence, the required current is0.093A

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Most popular questions from this chapter

20. The magnetic field inside a 5.0-cm-diameter solenoid is2.0T and decreasing at 4.0T/s. What is the electric field strength inside the solenoid at a point (a) on the axis and (b) 2.0cmfrom the axis?

The rectangular loop in FIGURE has 0.020惟resistance. What is the induced current in the loop at this instant?

A vertical, rectangular loop of copper wire is half in and half out of the horizontal magnetic field in FIGURE (The field is zero beneath the dashed line.) The loop is released and starts to fall. Is there a net magnetic force on the loop? If so, in which direction? Explain

I A 20-cm-long, zero-resistance slide wire moves outward, on zero-resistance rails, at a steady speed of 10m/sin a 0.10Tmagnetic field. (See Figure 30.26.) On the opposite side, a 1.0惟carbon resistor completes the circuit by connecting the two rails. The mass of the resistor is 50mg.

a. What is the induced current in the circuit?

b. How much force is needed to pull the wire at this speed?

c. If the wire is pulled for 10s, what is the temperature increase of the carbon? The specific heat of carbon is710J/kgK.

18. II FIGURE EX30.18 shows the current as a function of time through a 20 -cm-long, 4.0-cm-diameter solenoid with 400 turns. Draw a graph of the induced electric field strength as a function of time at a point 1.0cmfrom the axis of the solenoid.
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