Consider the current-carrying wires in the figure.
I can try to describe the figure here..
- Diagram A has the wire coming from the left, it forms a loop in the centre in a clockwise direction and leaves going to the right.
- Diagram B has the wire also coming from the left, it forms a loop in the centre counter- clockwise and leaves going to the right as well.
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?
a) BA < BB
b) BA = BB
c) BA > BB
d) There is not enough information to compare BA and BB
I guessed that both their magnitudes would be equal because the current and radius of both are equal; the only difference would be the direction of the magnetic fields, but this thinking is wrong..
I don't get how both wires can enter from the left and leave on the right unless either
(1) the circular part consists of 1 1/2 loops in both cases, or
(2) after making one loop and returning to the left end, both wires bend to leave at the right, following a diameter of the circle.
In either case, only the direction of the field at the middle should be different.
I'm sorry I can't help you with this. Maybe someone else can.
I must me missing something that would require seeing the figure to understand.
The answer 'B' is wrong?
But the only difference is direction of field.
I don't know if this might help to visualize: A's loop follows the way the greek letter gamma makes a loop, while B 's loop is in the shape of an upside down omega( Ω )...
wire A looks like
------o---
(consider that 'o' part is a continuous loop and -- represents wire))
wire B looks like
----(inverted omega, as sandra mentioned)---
i think Ba > Bb because in wire b there are some points where current changes direction and megnetic field is is reversed.
OK, I get it now. The straight parts of the incoming and outgoing wire are tangent to the loop. There IS a big difference in the field at the middle of the loop.
The higher B field is obtained at the middle in the "gamma loop" case because the B field produced by the straight sections of wires at the center of the loop is in the same direction as the field produced by the loop itself. In the other ("omega") case, they oppose each other at the center of the loop.
To determine the magnitude of the net magnetic field at the center of each loop, we can apply Ampere's Law. Ampere's Law relates the magnetic field around a closed loop to the current passing through the loop.
Let's start with Diagram A. In this case, the current flows in a clockwise direction around the loop. According to the right-hand rule (assuming conventional current flow), the magnetic field lines around the wire will be in the counterclockwise direction inside the loop. Applying Ampere's Law, we find that the magnitude of the magnetic field at the center of the loop, BA, is given by:
BA = (μ₀ * I) / (2 * R)
where μ₀ is the permeability of free space, I is the current, and R is the radius of the loop.
Now let's consider Diagram B. Here, the current flows in a counterclockwise direction around the loop. Following the right-hand rule, we find that the magnetic field lines around the wire will be in the clockwise direction inside the loop. Again applying Ampere's Law, the magnitude of the magnetic field at the center of the loop, BB, is given by:
BB = (μ₀ * I) / (2 * R)
Comparing the expressions for BA and BB, it's clear that they have the same magnitude and the same variables. Hence, we can conclude that (b) BA = BB is the correct statement. The direction of the magnetic field may be different in each case due to the current flow, but the magnitudes will be equal as long as the current and radius are the same.
Note: It's important to remember that in order to determine the direction of the magnetic field, we need to consider the right-hand rule and the direction of the current flow. The statement in the question only asks for the magnitude of the net magnetic fields, not their directions.