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Chapter 29: Q4P (page 856)

A straight conductor carrying current i=5.0Asplits into identical semicircular arcs as shown in Figure. What is the magnetic field at the center C of the resulting circular loop?

Short Answer

Expert verified

The magnetic field at the center isB=0.

Step by step solution

01

Given Information

Angle made by arc=蟺

02

Determining the formula for the magnetic field

Formula:

Magnetic field at center of circular arc is given by:

BC=渭04蟺脳i蠒R

Here, 蠒is the angle of arc and R is the radius of the arc.

03

Calculating the magnetic field at the center C of the resulting circular loop 

Magnetic field at center due to arc is given by:

B=渭04蟺脳i蠒R

Fields due to both arcs are opposite to each other.

Angle due to semicircular arcs =蟺,

Net field due to both semicircular arcs is

B=渭04蟺脳i蟺R+渭04蟺脳i-蟺R

B=0

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