Two long, straight, parallel wires are 1.00 m apart (Figure 1) . The wire on the

Question

Two long, straight, parallel wires are 1.00 m apart (Figure 1) . The wire on the left carries a current I1 of 6.00 A into the plane of the paper.

Figure 1)

A) What must the magnitude of the current I2 be for the net field at point P to be zero?

B) What must the direction of the current I2 be for the net field at point P to be zero? (EXPLAIN IT)

C) Then, what is the magnitude of the net field at Q?
D) What is its direction? (EXPLAIN IT)

E) Then, what is the magnitude of the net field at S?

Explanation / Answer

A) Use RHR to find the magnitude and direction of magnetic field at point P, B = uoI/(2pi*r)

B1 = B2 =====> (uo/2pi)(6/1.5) = (uo/2pi)(I2/0.5) ====> I2 = 2A

B) The direction of current I2 is out of the page to generate the B2 in opposite direction to B1 to make net field at P zero.

C) At Q,   B1 = uoI1/(2pi*r1) = (2*10^-7*6)/0.5 = 2.4*10^-6 T

B2 = uoI2/(2pi*r2) = (2*10^-7*2)/1.5 = 2.67*10^-7 T

net B = B1 - B2 = (2.4 - 0.267)*10^-6 = 2.133*10^-6 T

D) as field due to I1 is upward at Q and due to I2 is downward but B1> B2 so net field at Q is upwards

E) at S,   B1 = uoI1/(2pi*r1) = (2*10^-7*6)/0.6 = 2.0*10^-6 T

  B2 = uoI2/(2pi*r2) = (2*10^-7*2)/0.8 = 0.5*10^-6 T

both B1 and B2 are perpandicular so magnitude of bet field is = sqrt(22 + 0.52) *10^-6 = 2.062*10^-6 T

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