A bar of mass m rests perpendicularly on a pair of rails separated by a distance L that lie in the xy-plane, as shown. The bar is initially at the left edge of the rails at position x = 0. An external force moves the bar in the +x-direction at a constant speed v. The apparatus lies in a region of magnetic field B that is parallel to the xz-plane and points at an angle 0 to the left of the +x-axis. The magnitude B of the magnetic field decreases in the x-direction according to the equation Ba/(c+x), where a and c are positive constants. Derive an expression for the magnetic flux B(t) as a function of time t through the loop formed by the bar and rails. Define the normal to the loop to be in the +z-direction, and express your answer in terms of the given quantities. B(t) = = aL sin (0) In c+vt 9) In (c+w) e L
A bar of mass m rests perpendicularly on a pair of rails separated by a distance L that lie in the xy-plane, as shown. The bar is initially at the left edge of the rails at position x = 0. An external force moves the bar in the +x-direction at a constant speed v. The apparatus lies in a region of magnetic field B that is parallel to the xz-plane and points at an angle 0 to the left of the +x-axis. The magnitude B of the magnetic field decreases in the x-direction according to the equation Ba/(c+x), where a and c are positive constants. Derive an expression for the magnetic flux B(t) as a function of time t through the loop formed by the bar and rails. Define the normal to the loop to be in the +z-direction, and express your answer in terms of the given quantities. B(t) = = aL sin (0) In c+vt 9) In (c+w) e L
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter31: Gauss’s Law For Magnetism And Ampère’s Law
Section: Chapter Questions
Problem 72PQ
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Transcribed Image Text:A bar of mass m rests perpendicularly on a pair of rails
separated by a distance L that lie in the xy-plane, as shown.
The bar is initially at the left edge of the rails at position
x = 0. An external force moves the bar in the +x-direction
at a constant speed v.
The apparatus lies in a region of magnetic field B that is
parallel to the xz-plane and points at an angle 0 to the left of
the +x-axis. The magnitude B of the magnetic field
decreases in the x-direction according to the equation
Ba/(c+x), where a and c are positive constants.
Derive an expression for the magnetic flux B(t) as a
function of time t through the loop formed by the bar and
rails. Define the normal to the loop to be in the +z-direction,
and express your answer in terms of the given quantities.
B(t) =
=
aL sin (0) In
c+vt
9) In (c+w)
e
L
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