An insulated wire with mass m = 6.00 10-5 kg is bent into the shape of an invert

Question

An insulated wire with mass m = 6.00 10-5 kg is bent into the shape of an inverted U such that the horizontal part has a length l = 10.0 cm. The bent ends of the wire are partially immersed in two pools of mercury, with 2.5 cm of each end below the mercury's surface. The entire structure is in a region containing a uniform 0.00700-T magnetic field directed into the page (see figure below). An electrical connection from the mercury pools is made through the ends of the wires. The mercury pools are connected to a 1.50-V battery and a switch S. When switch S is closed, the wire jumps 30.0 cm into the air, measured from its initial position.

(a) Determine the speed v of the wire as it leaves the mercury. answer in  m/s

(b) Assuming that the current I through the wire was constant from the time the switch was closed until the wire left the mercury, determine I. answer in  A

(c) Ignoring the resistance of the mercury and the circuit wires, determine the resistance of the moving wire. answer in

Explanation / Answer

mass of the wire, m=6*10^-5 kg

length of the wire , l=10cm

magnetic field B=0.007 T

battery potential, V=1.5v

displacement of the wire, s=30cm

a)

use,

v^2=2*g*s

v^2=2*9.8*(30*10^-2)

====> speed v=2.42 m/sec

speed of the wire s it leaves the mercury, v=2.42 m/sec

b)

let,

current in the wire is i,

magnetic force(Fm) = gravitational forcr(Fg)

i*l*B=m*g

i*10*10^-2*0.007=6*10^-5*9.8

====> i=0.84 A

current in the wire is, i=0.84 A

c)

resistance R=V/i

R=1.5/(0.84)

R=1.78 ohms

resistance of the wire, R=1.78 ohms

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