Consider the current-carrying wires in the figure.
Both cases consist of long straight wires carrying a current I.
In both cases, the wire is also bent in the shape of a circular loop of radius R.
The only difference is in how the bending of the wire is done to create the loop.
We are interested in the magnitude of the net magnetic field at the center of the loop.
If BA and BB are the magnitudes of the net magnetic fields at the center of each loop respectively, then which of the following statements is true?
1)BA < BB
2)BA = BB
3)BA > BB
4)There is not enough information to compare BA and BB
I don't see the figure, so I don't know which loop might have more turns. If they are both one-turn loops with the same current and the same loop radius, then the B fields at the center are the same.
But, how can you make a circular loop if (as you say) the wire is straight?
I'll tell you the answer on Tuesday.
you forgot to take into account the field created by the long straight ends of the wire
yes the loops have current flowing in opposite direction so the field is in opposite direction
but in one situation, the field is additive with that created by the straight end of the wire, and in the other situation it subtracts from the other
if both wires current to the right
then they exert B in
the loop if current is counter clockwise makes B out, at the center
loop if current clockwise makes B in at the center
so the wire with clockwise has a higher B than the wire with counter clockwise
To determine the magnitude of the net magnetic field at the center of the loop for each case, we need to consider the contributions of the individual segments of the wire.
In case A, the wire is bent into a circular loop by curving it uniformly around the center. This creates a symmetrical configuration, where the magnetic field contributions from each segment of the wire cancel out at the center of the loop. The magnetic field vectors produced by adjacent wire segments are in opposite directions, resulting in complete cancellation. Therefore, the net magnetic field at the center of the loop in case A is zero.
In case B, the wire is bent into a circular loop by folding it in half and joining the ends. This creates an asymmetrical configuration, where the magnetic field contributions from each segment of the wire do not cancel out completely at the center of the loop. The magnetic field vectors produced by adjacent wire segments are not in opposite directions, resulting in a nonzero net magnetic field at the center of the loop.
Therefore, the true statement is:
3) BA > BB