21) (9 points) Consider two long, parallel wires. The first wire, carrying a ste

Question

21) (9 points) Consider two long, parallel wires. The first wire, carrying a steady current I = 2.0 A upward as shown n the figure to the right, is rigidly mounted and cannot move. The second wire, however, is mobile and moves directly away from the first wire. Both wires have a resistance per unit length (i.e., the total resistance of the wire divided by the length of the wire) of 0.25 ohm/m. Answer the following questions for the situation in which the second wire is momentarily at a distance d = 0.10 m from the first wire and is moving with a speed v = 3.0 m/s directly away from it. (a) The current I1, in the first wire produces a magnetic field that is experienced by the second wire. Calculate both the magnitude and the direction of this magnetic field at the location of the second wire. (b) A conductor moving through a magnetic field experiences an induced emf. Determine both the size and direction (up or down) of the current I2 induced n the second wire. (c) A conductor carrying a current in an external magnetic field experiences a force. Calculate both the magnitude and direction of the force per unit length on the second wire.

Explanation / Answer

a) magnetic field produed by the wire,

B = mue*I/(2*pi*d)

= 4*pi*10^-7*2/(2*pi*0.1)

= 4*10^-6 T

direction : into the page

b) induced emf = B*v*L

= 4*10^-6*3*L

= 12*10^-6*L

induced emf = induced emf/R

= 12*10^-6*L/(0.25**L)

= 4.8*10^-5 A

direction : down

c) Apply, force per unit length,

F/L = mue*I1*I2/(2*pi*d)

= 4*pi*10^-7*2*4.8*10^-5/(2*pi*0.1)

= 1.9210^-10 N

direction : right

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