Two insulated wires perpendicular to each other in the same plane carry currents

Question

Two insulated wires perpendicular to each other in the same plane carry currents as shown in (Figure 1) . Assume that I = 13 A and d = 13 cm .

A) Find the magnitude of the net magnetic field these wires produce at point P if the 10 A current is to the right (Current (a) in the figure). Express your answer in teslas to two significant figures.

B) Find the magnitude of the net magnetic field these wires produce at point Q if the 10 A current is to the right (Current (a) in the figure). Express your answer in teslas to two significant figures.

C) Find the magnitude of the net magnetic field these wires produce at point P if the 10 A current is to the left (Current (b) in the figure). Express your answer in teslas to two significant figures.

D) Find the magnitude of the net magnetic field these wires produce at point Q if the 10 A current is to the left (Current (b) in the figure). Express your answer in teslas to two significant figures.

Explanation / Answer

magnetic field is given by

B = u0*I/(2*pi*r)

r = distance from current

A)

two magnetic field are acting at point P. and both have same direction so

B = u0*13/(2*pi*0.13) + u0*10/(2*pi*0.08)

B = (4*pi*10^(-7)*13)/(2*pi*0.13) + (4*pi*10^(-7)*10)/(2*pi*0.08) = 45*10^(-6) T

direction is into the page (-z axis).

B)

two magnetic field are acting at point Q. and both have same direction so

B = u0*13/(2*pi*0.13) + u0*10/(2*pi*0.08)

B = (4*pi*10^(-7)*13)/(2*pi*0.13) + (4*pi*10^(-7)*10)/(2*pi*0.08) = 45*10^(-6) T

direction is out of the page (+z axis)

C)

two magnetic field are acting at point P. and both have different directions so

B = u0*13/(2*pi*0.13) (-k) + u0*10/(2*pi*0.08) (k)                                {k represents the direction of B (+z axis)}

B = (4*pi*10^(-7)*13)/(2*pi*0.13) (-k) + (4*pi*10^(-7)*10)/(2*pi*0.08) (k)

B = [- (2*10^(-7)*13)/(0.13) + (2*10^(-7)*10)/(0.08) ] (k) = 5*10^(-6) T

direction is out of the page (+z axis)

D)

two magnetic field are acting at point Q. and both have different directions so

B = u0*13/(2*pi*0.13) (k) + u0*10/(2*pi*0.08) (-k)

B = (4*pi*10^(-7)*13)/(2*pi*0.13) (k) + (4*pi*10^(-7)*10)/(2*pi*0.08) (-k)

B = [(2*10^(-7)*13)/(0.13) - (2*10^(-7)*10)/(0.08) ] (k) = 5*10^(-6) (-k) T

direction is into the page (-z axis)

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