Question
I just want to verify that my solutions to this problem are all correct and clear. If they're any errors what is the correct solution or Solutions?
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A solenoid has N 500 windings, radius a .10 m and height h 060 m; the current is found to be decreasing according to I(t) = 10-bt, where lo = 0.40 A and b = 0.200 A/s, and the current direction is shown in Figure 1. Calculate the rate at which electromagnetic energy is leaving the solenoid at t = 1.00 s. Answer this overarching question by answering the following set of guided questions N windingsh 1. Draw a careful cross-sectional picture of the solenoid, and using Ampere's Law derive an expression for the magnetic field inside the solenoid. Show your integration path on your figure. Your expression for the magnetic field will obviously be a function of time. 2. Now, since I(t) decreases with time, there will be an associated electric field set up inside the solenoid. Draw another cross-sectional picture showing the magnetic field and the electric field direction inside the solenoid. Figure 1: The solenoid in question. Radius is o.10 m and height is o.60 m 3. Use Faraday's Law to calculate the electric field inside the solenoid. Make sure that you show your path of integration and indicate the direction of the induced electric field. Now, to calculate the rate at which electromagnetic energy is leaving the system, we have to calculate the flux of the Poynting vector through the surface of the solenoid. 4 Calculate the direction and the magnitude of the Poynting vector at the surface of the solenoid (i.e. use the values of E and B at r a to calculate 5. Now calculate the flux through the surface area; this number is the rate 6. Show 7. Why don't we have to worry about the time rate of change of the electric the Poynting vector). Don't forget to include units. (in Watts) at which electromagnetic energy is leaving the solenoid magnetic field energy stored in the solenoid. field energy in the solenoid? that your answer to Question 5 is equal to the time rate of change of
Explanation / Answer
YOur solution to the problem is correct.I verified all the above calculations and found the same reuslts