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Terminal speed of a wire

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Question:

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

Show that the slide wire reaches a terminal speed $v_{\rm term}$

I know that , but how can I explained how it gets to this point in paragraph form.

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Answers:

Cramster Expert

hanu

(Cramster SME)

Cramster In-House Subject Matter Expert

Date Posted: 7/24/2008 7:33:43 AM Status: Live

Asker's Rating: Helpful

Response:

Given that the length of the moving wire is L

magnetic field is applied is B

mass of the wire is m

resistance in the moving wire is R

-------------------------------------------------------------------------------------

From the diagram it is clear that the velocity vector direction is perpendecular to the

magnetic field then θ = 90 degrees

if the wire of length is moving with velocity V in the magnetic field

the force on the wire is F = BILsinθ ------(1)

where I is the induced current .

if the wire of length is moving in magnetic field then the induced emf is

ε = BVL

then the induced current is I = ε /R

= BLV / R

from equation (1)

F = B(BLV / R)Lsinθ

mg = B(BLV / R)L (scince θ = 90)

= B²L²V/R

V = mgR /B²L²

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Terminal speed of a wire

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