We've got two long straight wires carrying current of 5A and placed along x and y axis respectively current flows in direction of positive axes we have to find magnetic field at a) (1 m,1 m)
b) (-1 m,1 m)
c) (-1 m,-1 m)
d) (1 m,-1 m)
now using ampere's law $$ \oint_{}^{}B.dl=\mu_oi $$ i found magnetic field for infinite wire be $$ B=\frac{\mu_oi}{2\pi r}$$ where r is distance from the wire but for evaluating the magnetic field we need to know direction of it and thus add it like vector but finding direction of magnetic feild at these point is confusing me , how do i find proper direction of magnetic field ?
[Physics] How to find the direction of the magnetic field for an infinite conducting wire
electricityelectromagnetismhomework-and-exercisesmagnetic fields
Related Solutions
Moving charge always produces a magnetic field. If you have a non-zero current then you have non-zero moving charge and a magnetic field will be produced.
You can achieve essentially no magnetic field though by using two wires right next to each other each carrying current in the opposite directions. As long as the wires are very close and the amount of current they carry is very close the magnetic fields they produce will nearly cancel. This is why a clamp meter can't measure current around two conductors carrying current in opposite directions.
You have been tricked by the way this has been drawn. Rotating the wire whilst keeping it perpendicular to the magnetic field does not change the magnitude of the force. Only when you change the angle between the wire and the field, i.e. tilt the wire so that it lines up with the field, does the magnitude reduce.
To prove this, we can look at the origin of this force. It arises directly from the Lorentz force on the electrons in the wire, and is given for each electron by $\textbf F = q(\textbf E + \textbf v \times \textbf B)$. The magnetic contribution to this force is a cross product of the velocity (which is essentially the current) and the field direction: $\textbf v \times \textbf B = vB\sin\theta$. Here $\textbf v$ and $\textbf B$ are perpendicular so the force on each electron is exactly equal to $vB$, which of course translates to $BIL$ on the wire.
Just in case this is still not clear to you, I made a 3D diagram of the situation in the question. The red lines represent the uniform magnetic field, the yellow line is the wire and the green arrow is the force.
As you can see the magnitude of the force does not change as the wire is rotated perpendicularly. However, if we were to rotate in the other direction, the cross product of $\textbf v \times \textbf B$ would have an affect on the magnitude of the force. This can be seen below.
I hope this was useful. OpenSCAD source code:
$fn=30;
for (x=[-10:5:10]) for (y=[-10:5:10])
translate([x, y, 0])
color("red")
translate([0, 0, -10])
cylinder(d=0.5, h=20);
theta = 360*$t;
alpha = 90;//*$t;
f = 10*sin(alpha); //[BIL]sin(theta)
color("green")
rotate(theta)
rotate([90, 0, 0]) {
cylinder(d=1, h=f);
translate([0, 0, f])
cylinder(d1=3, d2=0, h=2);
}
color("yellow")
rotate(theta)
rotate([0, alpha, 0])
translate([0, 0, -10])
cylinder(d=1, h=20);
(gif created with convert -resize 40% -delay 5 -loop 0 frame* gif1.gif)
Best Answer
The quickest way would be to use the right hand grip rule. From symmetry you may conclude that the magnetic field around each wire forms concentric circular loops around the wire. So now it remains to determine whether clockwise or anticlockwise. To do this, just imagine that you are gripping the wire with your right hand in such a way that your thumb points in the direction of current. Then the remaining fingers point in the direction of the magnetic field. This follows directly from the convention used for doing path integrals - if the closed line integral is performed in the anti-clockwise direction, then the area vector for doing the corresponding surface integral is taken to point towards you. Of course, having thus found the contributions from each individual wire, you would then have to take their vector sum.
On a side note, similar conventions are adopted in mechanics for finding the direction of angular velocity corresponding to clockwise or anticlockwise rotation. Thankfully, the convention is more or less uniform through all areas of physics!