Average Induced EMF in Loop of Wire Rotated in B-Field

In summary, a loop of wire with a 7.2 cm diameter initially perpendicular to a 1.3 T magnetic field is rotated in 0.20 s to become parallel to the field. The average induced emf in the loop is calculated using the formula ФB = BA and the value of A is found to be 0.004 m. The change in dot product of the vectors is taken into consideration and the root mean square voltage is calculated by multiplying the calculated value of ФB by 1/root(2).
  • #1
airkapp
58
0
A 7.2 cm diameter loop of wire is initially oriented perpendicular to a 1.3 T magnetic field. It is rotated so that its plane is parallel to the field direction in .20 s. What is the average induced emf in the loop?

A = πr2

A = π*.001 = .004 m

ФB = BA

= (1.3T)(.004m) = 5.2E-3 Wb

ФB / t = 0-5.2E-3 Wb / .20 s

= -2.6E-2 Wb/s

€ = -(1)( -2.6E-2 Wb/s)

= 2.6E-2 V


I think i messed up in my area of my formula. can someone help me out here.
 
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  • #2
I don't see any trig functions there... because the loop is rotated, there has to be a change in the dot product of the vectors.

Remember that A . B = |A| |B| cos theta
 
  • #3
Now that I think about it - can't you just take BA/t and then times it by 1/root(2) to get the root mean square voltage.
 

What is the average induced EMF in a loop of wire rotated in a B-field?

The average induced EMF in a loop of wire rotated in a B-field is equal to the rate of change of the magnetic flux through the loop. This can be calculated using the formula E = -N(dΦ/dt), where E is the average induced EMF, N is the number of turns in the loop, and dΦ/dt is the change in magnetic flux over time.

How does the average induced EMF change if the loop of wire is rotated at a faster rate?

If the loop of wire is rotated at a faster rate, the average induced EMF will also increase. This is because the change in magnetic flux through the loop is greater, resulting in a larger value for dΦ/dt in the formula E = -N(dΦ/dt).

Does the size or shape of the loop of wire affect the average induced EMF?

Yes, the size and shape of the loop of wire can affect the average induced EMF. A larger loop will have a greater area, resulting in a larger change in magnetic flux and a higher average induced EMF. Similarly, the shape of the loop can also impact the average induced EMF, as a non-circular loop may have a varying magnetic flux through different areas of the loop.

What is the relationship between the strength of the B-field and the average induced EMF?

The strength of the B-field is directly proportional to the average induced EMF. This means that as the strength of the B-field increases, the average induced EMF will also increase, assuming all other variables remain constant.

Can the direction of rotation of the loop of wire affect the average induced EMF?

Yes, the direction of rotation of the loop of wire can affect the average induced EMF. This is because the direction of rotation can change the direction of the change in magnetic flux through the loop, resulting in a positive or negative value for dΦ/dt in the formula E = -N(dΦ/dt). This, in turn, affects the magnitude and direction of the average induced EMF.

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