Mag force between two wires with opposite charges

[fm621]

Homework Statement

Two wires shown in figure p19.48 carry currents of 5.00A in opposite directions and are separated by 10cm. Find direction and magnitude of the net mag field.

(a) at a point midway between the wires. (b) at point P1 (c) at point P2

Homework Equations

B=B1+B2??
B= u0I / 2pir

The Attempt at a Solution

How would i approach a question like this? How does opposite charges affect the sign in the equation B1+B2?

Thanks!

 

[merryjman]

The equation you cite is for the magnetic field due to a long straight wire

$$\vec{B} = \frac{\mu I}{2 \pi R}$$

and as you state, the total magnetic field is the vector sum of the two individual fields.

The fact that the currents move in opposite directions will change the direction of the magnetic field lines for one wire vs. the other. You can use the right hand rule for wires to figure these directions out. For example, if you were looking directly down the length of a wire that was carrying current towards you, the magnetic field lines would be counterclockwise circles (point your thumb at your face and your fingers curl in the cc direction). If the wire carried current away from you, the field would be clockwise.

 

[fm621]

so for the first part (a):

B=B1-B2

B1= u5A / 2pi(.05)
B2= (u5A / 2pi(.05)

B= (u5A / 2pi(.05)) - (u5A / 2pi(.05))
the magnitude of the field in part a would be zero??

 

[merryjman]

No, using the RHR you should find that between the wires the fields actually add together and their direction points into the page. At points P1 and P2 the fields are in opposite directions and therefore subtract.

This is why the power supply wires inside a computer are twisted together. Since the power and return wires carry current in opposite directions, twisting them together makes the magnetic fields almost completely cancel out.

 

[fm621]

maybe i need practice with the right hand rule lol

when i apply the rhr for the first wire, my thumb points north and fingers clockwise

when i apply the rhr for the second wire, my thumbs point south and the fingers counter clockwise.

how exactly is direction changing with distance? this is frustrating haha

 

[merryjman]

You did the RHR correctly, but in between the wires the clockwise direction from the first wire gives you a field that points into the page on the right side of it (i.e. in between the wires) and the same is true for the second wire.

 

[fm621]

ok so let me understand,

for (a)

B=-B1-B2

for (b)

B=-B1+B2

for (c)

B=B1-B2

is this how it would be?

 

[merryjman]

yes, that should give you the correct magnitudes.