Magnetic field due to electric wire

[Silver2007]

Homework Statement

Find the magnetic field at point P.

Relevant Equations

B_P = 2B(R, pi/4)

In my opinion, the magnetic field at point P should cancel each other, because the magnetic field caused by the two wires has the same direction, like this.

but the solution does not assume that the magnetic fields cancel each other out. I don't know where I'm wrong, please help me, thanks.

 

[BvU]

Hello @Silver2007 ,

​

In your 'like this' picture the currents in the wires are parallel. But in your exercise they are not -- check for each of the two wires whether the B field points into or out of the paper

[edit] and your video continues with the case where one of the currents is in opposite direction. But I'm getting swamped with commercials, so I'm not going to look at it in deetail

$\$

 

[Silver2007]

Hello @Silver2007 ,

​

In your 'like this' picture the currents in the wires are parallel. But in your exercise they are not -- check for each of the two wires whether the B field points into or out of the paper

[edit] and your video continues with the case where one of the currents is in opposite direction. But I'm getting swamped with commercials, so I'm not going to look at it in deetail

$\$

I used the right hand rule and found that each wire's magnetic field points out of the paper. Thus, the superposition of magnetic fields at point P will have to cancel each other.

 

[SammyS]

I used the right hand rule and found that each wire's magnetic field points out of the paper. Thus, the superposition of magnetic fields at point P will have to cancel each other.

The magnetic field points out of the paper for each wire. That's correct. But no, they do not cancel.

 

[Silver2007]

The magnetic field points out of the paper for each wire. That's correct. But no, they do not cancel.

Why don't they cancel each other out? Can you explain in more detail? Thanks.

 

[BvU]

Do you know how to add two vectors?

 

[Orodruin]

Why don't they cancel each other out? Can you explain in more detail? Thanks.

If both vectors point out of the paper, then it is impossible for them to cancel. For there to be a cancellation one would have to point out of and the other into the paper.