In the figure below, four long copper wires are perpendicular to the page, and t
ID: 2060478 • Letter: I
Question
In the figure below, four long copper wires are perpendicular to the page, and their cross sections form a square of edge length a = 13 cm. The currents are out of the page in wires 1 and 4, and into the page in wires 2 and 3, and each wire carries 16 A. In unit-vector notation, what is the net magnetic field at the square's center? (Take the positive direction of the z axis to be out of the screen. Substitute numeric values, do not use variables.) Answer in units of T.
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Explanation / Answer
Distance of mid-point from corner =(13^2+13^2)/2 = 9.1924 cm
Magnetic Field produced by each wire has magnitude:
B=4*10^-7*16/2*9.1924*10^-2
=3.84114*10^-5 T
Direction of magnetic Field:
By wire 1 = towards point 2
By wire 2= towards point 1
By wire 3= towards point 2
By wire 4 =towards point 1
Net magnetic field towards 2 =B2=2*B= 6.96227*10^-5
Net magnetic field towards 1 =B1=2*B= 6.96227*10^-5
These two arre perpendicular two each other and has same magnitude.
B(net)=B1^2+B2^2
=9.8461*10^-5 T
Direction of this magnetic field is along the positive y-axis.
B(net)= 9.8461*10^-5 j