A solenoid runs though the x-y plane with 2x meter) with some in the xy plane, i

Question

A solenoid runs though the x-y plane with 2x meter) with some in the xy plane, in the solenoid. It is then changed into an equilateral triangle wrapped once using all the wire from the 10/m turns per meter) with some current in it which is constant. A wire wrapped once into a square with sides of 0.73 meters is placed the x-y plane, in the solenoid. It is then changed into an equilateral triangle wrapped once using all clockwise around direction of the current? Indicate the clockwise direction with a negative sign the triangular wire. If the time taken to reshape the wire is 0.15 seconds and its resistance is 5 Ohms what is the current in the solenoid in amps, and what is the square. This induces an average current of 8 mill-amps

Explanation / Answer

a = length of each side of the square loop = 0.73 m

As = area of square loop = a2 = 0.732 = 0.533 m2

L = length of side of equilateral triangle

length of the wire remain same , hence

circumference of triangle = circumference of square

3L = 4 a

3 L = 4 (0.73)

L = 0.973 m

At = area of the triangle = sqrt(3) L2/4 = sqrt(3) (0.973)2/4 = 0.410 m2

i = induced current in triangle = 8 mA = 0.008 A

R = resistance = 5 ohm

induced emf is given as

E = i R = 0.008 x 5 = 0.04 Volts

t = time = 0.15 sec

change in magnetic flux is given as

deltaPhi = - E t = - 0.04 x 0.15 = - 0.006

B = magnetic field

deltaA = change in area = At - As = 0.410 - 0.533 = - 0.123 m2

deltaPhi = B deltaA

- 0.006 = B (- 0.123)

B = 0.0488 T

n = number of turns per unit length = 20000

I = current in solenoid = ?

Using the equation

B = uo n I

0.0488 = (12.56 x 10-7) (20000) I

I = 1.94 A clockwise

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