Question

Part A 

What is the magnetic field strength at point 1 in the figure? (Figure 1) 

Part B 

What is the magnetic field direction at point 1 in the figure? 

Part C

What is the magnetic field strength at point 2 in the figure?

Part D

What is the magnetic field direction at point 2 in the figure?

Part E

What is the magnetic field strength at point 3 in the figure?

Part F

What is the magnetic field direction at point 3 in the figure?

Answer 1

A) We know that magnetic field strength, B = $\mu$_oI/2r, where $\mu$_o = 4pi*10^-7, I is the current, r is the distance of the point from the current carrying wire.

At point 1, net B = magnetic field due to current in top wire + magnetic field due to current in bottom wire = B1+(-B2)

= (4pi*10^-7*10/2pi*0.02 ) - (4pi*10^-7*10/2pi*0.06) = 6.67*10^-5T

B2 is negative because it is in the opposite direction (pointing into the page), but since it is further way, the net magnetic field is out of the page.

B) Magnetic field direction at point 1 is out of the page as described above.

C) Magnetic field strength at point 2 is

B(total)=B1+B2=(4pi*10^-7)(10)/(2pi*0.02) + (4pi*10^-7)(10)/(2pi*.02)=2.0*10^-4 T (into page)

Both B1 and B2 point into the page, hence net field is into the page.

D) Magnetic field direction at point 2 is out of the page as described above.

E) Magnetic field strength at point 3 is

B(total)=B1+B2=(4pi*10^-7)(10)/(2pi*0.02) - (4pi*10^-7)(10)/(2pi*.06)= 6.67*10^-5T (out of the page)

F) B2 is negative because it is in the opposite direction (pointing into the page), but since it is further way, the net magnetic field is out of the page