A long rectangular conducting wire loop of width, L resistance, R and mass, m is

Question

A long rectangular conducting wire loop of width, L resistance, R and mass, m is arranged horizontally as shown in the figure. A uniform magnetic field, B is directed into the page and exists only in the region above dashed line, a. The loop is dropped and during its fall, it accelerates until it reaches its terminal speed, v(. You may ignore air resistance. Using Faraday's Law, determine an expression that relates the potential difference generated about the loop (commonly referred to as EMF), E to the terminal speed, v_t. Give an expression for any force exerted on the loop resulting from a current flowing in it, and illustrate it's direction in a sketch. Combining your results of parts (i) and (ii), determine an expression for v, in terms of L, R, m, B and the acceleration due to gravity, g. The cross sectional diameter of the conducting wire is increased by a factor of three. Determine if this increases or decreases v,, and by what factor it is v, changed.

Explanation / Answer

1)

E = d(BA)/dt

E = BdA/dt

E = BVL

2)

current

i = E/R

i = BVL/R

3)

Fb = i LB

Fg = mg

Fb= Fg

B^2 L^2 V /R = mg

V = mgR/B^2L^2

4)

since R is inversely proportional to radius square

V1 = V/9

by factor 9

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