A straight conductor of length is placed along the -axis from to and carries a steady…

PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Magnetic Fields and Electromagnetism · Magnetic Fields and Electromagnetism

Problem

A straight conductor of length

L

is placed along the

x

-axis from

x=0

x=L

and carries a steady current

I

in the positive

x

-direction. The magnetic field in the region is non-uniform and is given by

\mathbf{B}=k x\,\hat{j}

where

k

is a positive constant and

\hat{j}

is the unit vector along the

y

-axis. (i) Obtain an expression for the differential force acting on an element of the conductor located between

x

and

x+dx

. Hence derive an expression for the total magnetic force on the entire conductor. (ii) Determine the

x

-coordinate of the point along the conductor through which the net force can be considered to act (i.e. the line of action of the resultant force). (iii) Calculate the torque about the origin

O(0,0,0)

due to the magnetic forces on the conductor.

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