Magnetic Field Strength & Direction at Points 1-3

[cemar.]

1. What are the magnetic field strength and direction at points 1 to 3 in the figure?
Okay, sorry, once again i don't know how to get the picture up here so ill describe it!
There are 2 long wires 4 cm apart, the one on top with a current of 10 A in the positive x direction and the one on the bottom with a current of 10 A in the negative x direction.
Point 1 is 2cm above the top wire.
Point 2 in directly in between the two wires.
Point 3 is 2cm underneath the bottom wire.

Homework Equations

Okay so here I am thinking something along the lines of that B = (u0/4pi)(Is 'r-hat'/r^2)
or maybe i found this equation in my notes that could be helpful and my gut says its the better bet
B = (u0I)/(2pid)

The Attempt at a Solution

Point 1 : (u0*10A)/(2pi*0.02m)
Point 2 : since it is inbetween two wires with opposite currents, so opposite fields (?) my guess is that it is equal to 0?
Point 3 : the opposite of point 1

Im also curious as to whether we assign a negative or positive value to the current??
And also would the bottom wire have an effect on the magnetic field at point 1??

 

[rl.bhat]

You have to decide the direction of the field by right hand clasp rule. Accordingly the field at point 1 due to top wire is coming out of the paper at a distance 2 cm from the wire and field due to bottom wire is going into the paper at a distance 6 cm from this wire. Apply the same rule to the other points.

 

[Moetasim]

The magnetic field strength and direction at points 1 to 3 can be calculated using the right-hand rule and the equations you have mentioned. At point 1, the magnetic field is directed towards the left (negative x direction) due to the current in the top wire. The strength of the magnetic field can be calculated using the equation B = (u0I)/(2pi*r) where I is the current in the wire, r is the distance from the wire, and u0 is the permeability of free space. So at point 1, the magnetic field strength would be B = (4pi*10 A)/(2pi*0.02 m) = 200 uT (microtesla) towards the left.

At point 2, the magnetic field would be cancelled out due to the opposite currents in the two wires. So the magnetic field strength would be zero.

At point 3, the magnetic field would be directed towards the right (positive x direction) due to the current in the bottom wire. The strength of the magnetic field can be calculated using the same equation as before, B = (u0I)/(2pi*r), but with a negative sign since the current is in the opposite direction. So at point 3, the magnetic field strength would be B = -(4pi*10 A)/(2pi*0.02 m) = -200 uT towards the right.

As for assigning a positive or negative value to the current, it depends on the direction of the current flow. In this case, the current in the top wire is in the positive x direction, so it would have a positive value. The current in the bottom wire is in the negative x direction, so it would have a negative value.

The bottom wire would have an effect on the magnetic field at point 1, as the magnetic field lines from both wires would interact and create a resultant magnetic field at that point. This can be seen in the equation B = (u0I)/(2pi*r) where r is the distance from the wire. So the magnetic field at point 1 would be affected by both wires.