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Chapter 31: Q. 37 (page 902)

A 10A current is charging a 1.0-cm-diameter parallel-plate capacitor.

a. What is the magnetic field strength at a point 2.0mmradially from the center of the wire leading to the capacitor?

b. What is the magnetic field strength at a point localid="1650010280999" 2.0mmradially from the center of the capacitor?

Short Answer

Expert verified

a) The magnetic field strength at a point 2.0mmradially from the center of the wire leading to the capacitor isB=0.001T.

b) The magnetic field strength at a point2.0mmradially from the center of the capacitor isB=16×10-5T.

Step by step solution

01

Part(a) Step 1: Given information

We are given that Current I=10A

Radius of platelocalid="1650010296361" R=0.5×10-2m

02

Part(a) Step 2: Simplify

Magnetic field strength due to current carrying conductor from the center of the wire.

B=μoI2πrr=4π×10-7×102π×2×10-3=10-3T

B=0.001T

03

Part(b) Step 1: Given information

We are given thatI=10A

r=2×10-3cm

R=0.5×10-2cm

04

Part(b) Step 2: Simplify

Magnetic field from the center of capacitor

B=μoIr2πR2=4π×10-7×10×2×10-32π×(0.5×10-2)2

B=16×10-5T

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Most popular questions from this chapter

FIGUREP31.38shows the voltage across a 0.10mFcapacitor. Draw a graph showing the displacement current through the capacitor as a function of time.

What is the force (magnitude and direction) on the proton in FIGURE P31.29? Give the direction as an angle CWor cCWfrom vertical.

The magnetic field is uniform over each face of the box shown in FIGUREEX31.6. What are the magnetic field strength and direction on the front surface?

FIGUREP31.39Shows the electric field inside a cylinder of radius localid="1649879543758" R=3.0mm.. The field strength is increasing with time as localid="1649879549377" E=1.0×108t2V/m, where tis in s. The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for localid="1649879554833" t<0.

localid="1649879566359" a.Find an expression for the electric flux localid="1649879560575" ϕethrough the entire cylinder as a function of time.

localid="1649879572467" b. Draw a picture showing the magnetic field lines inside and outside the cylinder. Be sure to include arrowheads showing the field’s direction.

localid="1649879587867" c. Find an expression for the magnetic field strength as a function of time at a distance localid="1649879577475" r<Rfrom the center. Evaluate the magnetic field strength atlocalid="1649879582437" r=2.0mm, localid="1649879592577" t=2.0s.

d. Find an expression for the magnetic field strength as a function of time at a distancelocalid="1649879597467" r>Rfrom the center. Evaluate the magnetic field strength at localid="1649879602321" r=4.0mm, localid="1649879607075" t=2.0s.

A radio receiver can detect signals with electric field amplitudes as small as 300μV/m. What is the intensity of the smallest detectable signal?
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