How Does Solenoid Turn Density Affect Induced EMF in a Nearby Loop?

[xcvxcvvc]

didn't convert cm to m

Homework Statement

A solenoid has 10 turns/cm and carries a 4-A current. A circular loop with 5 turns of area i cm^2 lies within the solenoid with its axis at 37 degrees to the axis of the solenoid. Find the magnitude of the average induced emf if the current increases by 25% in .1 seconds.

Homework Equations

emf = N * d(flux)/dt
flux = B dot da

The Attempt at a Solution

I'm confused about why the solenoid's area is not given. How is the loop's area relative to the solenoid's area not relevant?

Here's what I tried:
emf = N d(flux)/dt
= (N * A * cos(theta)) * (B(final) - B(initial))/(deltaT)
and B for a solenoid is

so (N * A * cos(theta) * μ * n) * (I(f) - I(i))/(deltaT)
then ( 5 * 8 * cos(37) * 4 * pi * 10^-7 * 10) * (4 * 1.25 - 4)/ .1=4mV

the answer is in microvolts, so I'm obviously doing something completely wrong

 

[anathema]

. Can someone please help me out?

Hello,

It seems like you may have forgotten to convert the units for the solenoid's area from cm^2 to m^2. Remember, in order to use the formula for flux (B dot da), all units must be in meters. Additionally, the units for the current should also be in amperes, not milliamperes.

To convert cm^2 to m^2, you can use the conversion factor 1 cm = 0.01 m. So, the solenoid's area would be 0.08 m^2.

Also, keep in mind that the units for magnetic field strength (B) are teslas (T), not webers (Wb). So, when you calculate the final and initial magnetic fields, make sure to use the correct units.

Once you make these conversions, your final answer should be in microvolts. I hope this helps!

 

[kerimek]

.

As a scientist, it is important to pay attention to all the given information in a problem and make sure all units are consistent. In this case, the area of the solenoid is not given, but it is still relevant because it affects the magnetic field and therefore the flux and emf. Additionally, it is important to convert all units to the appropriate SI units, such as converting cm to m.

To solve this problem correctly, we need to first calculate the magnetic field inside the solenoid. Using the equation B = μ0 * n * I, where μ0 is the permeability of free space, n is the number of turns per unit length, and I is the current, we can calculate the magnetic field to be B = 4π * 10^-4 T.

Next, we can calculate the flux through the circular loop using the equation Φ = B * A * cos(θ), where A is the area of the loop and θ is the angle between the magnetic field and the normal to the loop. Since the loop is at an angle of 37 degrees to the axis of the solenoid, we can use cos(37) = 0.8. The area of the loop is given in cm^2, so we need to convert it to m^2 by dividing by 10,000. This gives us a flux of Φ = 0.8 * 5 * 10^-4 Wb.

Now, we can calculate the average induced emf using the equation emf = N * ΔΦ/Δt, where N is the number of turns in the loop, ΔΦ is the change in flux, and Δt is the change in time. In this case, since the current increases by 25% in 0.1 seconds, Δt = 0.1 seconds and ΔΦ = 0.8 * 5 * 10^-4 Wb * 0.25 = 0.1 * 10^-4 Wb. Therefore, the average induced emf is emf = 5 * 0.1 * 10^-4/0.1 = 5 * 10^-4 V = 500 μV.

In conclusion, it is important to carefully consider all the given information and make sure all units are consistent when solving a problem in science. In this case, by paying attention to the units