physics test review question #4 help!~ plz!ansewer step by step 1. [a] Use Amper

Question

physics test review question #4 help!~

plz!ansewer step by step

1. [a] Use Ampere's Law to show that the magnetic field at a point a distance r from a long straight wire carrying a current I is given by B HoI/2Tr [b] Show that the magnitude of the force per unit length between a pair of parallel conductors a distance r apart and carrying currents I and I is given by: B Fo 1 Indicate the direction of the f when the 2 ztr currents are in the same direction and when they're in opposite directions. [c] Two long, parallel wires repel one another with a force per unit length of 60x10 Nlm ne of the wires carries a current of 4.0 A and the current in the second wire is 3.0 A how far apart are the wires Id] Are the currents in the two wires in part [c] flowing in the same or opposite directions?

Explanation / Answer

a) According to Ampere's law

integral B.dl = mue*Ienclosed

consider a cirlce with radius r around the wire

B integral dl = mue*I

B*L = mue*I

B*2*pi*r = mue*I

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

b) Force on second wire, F = B*I2*L*sin(90)

= (mue*I1/2*pi*r)*I2*L

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

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

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

= 4*pi*10^-7*4*3*/(2*pi*6*10^-5)

= 4*10^-2 m

= 4 cm

d) they are repeling each other. it means current is opposite in direction.

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