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FIGURE shows a U-shaped conducting rail that is oriented vertically in a horizontal magnetic field. The rail has no electric resistance and does not move. A slide wire with mass mand resistance Rcan slide up and down without friction while maintaining electrical contact with the rail. The slide wire is released from rest.

a. Show that the slide wire reaches a terminal speed vterm, and find an expression forvterm .

b. Determine the value of vtermif l=20cm,m=10g,R=0.10and B=0.50T

Short Answer

Expert verified

(a) Expression of Terminal velocity, vterm=mgRB2l2

(b) Value of Terminal velocity,vterm=0.98m/s

Step by step solution

01

Find expression for Vterm  (part a)

The rod is determined by two forces: an upward magnetic force and a downward weight force. When the two forces are balanced, the velocity becomes constant.

FB=mg

When a current-carrying wire moves through a magnetism, the field imposes a magnetic pull on the wire. The magnetic force exerted by a wire of length is described by an equation.

FB=IlB

02

Using Faraday's law

Using Faraday's law to get the magnitude of emf in terms of moving antenna using equation,

=Blv

Using Ohm's law to get the Induced current

I=R=BlvR

Use this expression to get the magnetic force,

FB=IlB=BlvRlB=B2l2vR

As FB=mg, so we use equation (4) to get the terminal velocity bymg=B2l2vtermR

vterm=mgRB2l2
03

Find Terminal velocity (part b)

vterm=mgRB2l2

=1010-3kg9.8m/s2(0.10)(0.50T)2(0.20m)2

=0.98m/s

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