What are the magnetic field strength and direction at points 1 to 3 in the figur

Question

What are the magnetic field strength and direction at points 1 to 3 in the figure below, in which I = 7 A, d = 5 cm, and D= 10 cm?

a) What is the magnetic field strength and direction at point 1 due to the top wire?
B due to top wire:____________ T,  --Direction-- up down right left out of page into page

b) What is the magnetic field strength and direction at point 1 due to the bottom wire?
B due to bottom wire: ___________ T,  --Direction-- up down right left out of page into page

c) What is the net magnetic field strength and direction at point 1?
net B at point 1: ____________ T,  --Direction-- up down right left out of page into page

d) What is the net magnetic field strength and direction at point 2?
net B at point 2: ___________ T,  --Direction-- up down right left out of page into page

Explanation / Answer

a)

Here , due to top wire ,

magnetic field at 1 ,

B1 = u0*I/(2*pi*d)

B1 = 4pi*10^-7 * 7/(2 * pi * 0.05)

B1 = 2.801 *10^-5 T

the magnetic field at the point 1 due to top wire is 2.801 *10^-5 T

and the field is out of the page

b)

due to bottom wire ,

B1 = u0*I/(2*pi*(d+D))

B1 = 4pi*10^-7 * 7/(2 * pi * 0.15)

B1 = 0.933 *10^-5 T

the magnetic field at the point 1 due to bottom wire is 0.933 *10^-5 T

and the field is into the page

c)

magnetic field at point 1 ,

B1net = magnetic field due to top + magentic field due to bottom

B1net = 2.801 *10^-5 - 0.933 *10^-5 T

B1net = 1.868 *10^-5 T

the net magnetic field at 1 is 1.868 *10^-5 T

the direction of field is out of the page

d)

at point 2 ,

B2 = Btop + Bbottom

B2 = 2 * u0 * I/(2 * pi* D/2)

B2 = 4 * 4pi *10^-7 * 7/( 2 * pi * 0.10)

B2 = 5.6 *10^-5 T

the direction of magnetic field is INTO the page

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