Magnetic Field in a Rectangular Conducting Loop

In summary, the problem involves a rectangular conducting loop being pulled through two regions of uniform magnetic field. The current induced in the loop is given by a function of its position. The magnetic field in region 1 is found to be 3.64 microT and in region 2 to be 1.21 microT, both pointing out of the page. The mistake in finding the magnetic field in region 2 was corrected by taking into account the induced current in both regions.
  • #1
daimoku
20
0
[SOLVED] Magnetic Field in a Rectangular Conducting Loop

Homework Statement


Figure 31-64a shows a rectangular conducting loop of resistance R = 0.010 , height H = 1.5 cm, and length D = 2.5 cm being pulled at constant speed v = 55 cm/s through two regions of uniform magnetic field. Figure 31-64b gives the current i induced in the loop as a function of the position x of the right side of the loop. For example, a current of 3.0 µA is induced clockwise as the loop enters region 1. What are the magnitudes and directions of the magnetic field in region 1 and region 2?

http://personalpages.tds.net/~locowise/test/W0736-N.jpg

Homework Equations


[tex] EMF=BLV [/tex]

[tex] i=EMF/R [/tex]

The Attempt at a Solution


Okay, I found the magnetic field in region 1 like so:
3*10^-6A = EMF / 0.010 ohms
EMF=3*10^-8 V

3*10^-8 V = B * 0.015m * 0.55 m/s
B = 3.64 microT for region 1

However, for region 2 I must be making a mistake somewhere. Could someone point out my mistake please? Here's what I tried:

-2*10^-6A = EMF/ 0.010 ohms
EMF = 2*10^-8 V
EMF=BLV
2*10^-8V = B * 0.55 m/s * 0.015m
B=2.42 microT

I have a feeling the mistake is in the length but I don't entirely understand how to interpret the problem statement. Thanks for your help!
 
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  • #2
I tried taking the difference between magnetic fields 1 and 2 but it doesn't seem to be working. Can anyone offer some help?
 
  • #3


I realize this post is over two years old, but for anybody who cannot figure out this problem and stumbles across this page, here is the answer for region 2.

EMF(2) = i(1)R + i(2)R = R[ i(1) + i(2) ] = (0.010 ohm)[(3*10^-6A) + (-2*10^-6A)]
EMF(2) = 1*10^-8V

Then use the same equation that daimoku was using to find B(2) for region 2.

B(2) = EMF(2) / (v * H) = (1*10^-8) / (0.55m/s * 0.015m) = 1.21 microT.

Both B(1) and B(2) are out of the page.
 

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges or by the intrinsic magnetic properties of certain materials.

2. How is a magnetic field created in a rectangular conducting loop?

A magnetic field is created in a rectangular conducting loop by passing an electric current through the loop. The direction of the magnetic field is perpendicular to the direction of the current flow and is strongest at the center of the loop.

3. What is the direction of the magnetic field in a rectangular conducting loop?

The direction of the magnetic field in a rectangular conducting loop is determined by the right-hand rule. If the current flows clockwise in the loop, the magnetic field will point outwards from the loop. If the current flows counterclockwise, the magnetic field will point inwards towards the loop.

4. How does the shape of a rectangular conducting loop affect the magnetic field?

The shape of a rectangular conducting loop affects the magnetic field in two ways. Firstly, the closer the loop is to a perfect rectangle, the more uniform the magnetic field will be within the loop. Secondly, the larger the loop, the stronger the magnetic field will be at the center.

5. What are some applications of a magnetic field in a rectangular conducting loop?

Magnetic fields in rectangular conducting loops are used in a variety of applications, including electric motors, generators, and magnetic resonance imaging (MRI) machines. They can also be used to measure the strength of electric currents and to create electromagnetic waves for communication purposes.

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