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19. An infinite solenoid with a radius of 7 cm is driven by an AC power source. The maximum magnetic field inside is 5 mT, and it is driven sinusoidally at 60 Hz. We will determine the induced electric field everywhere. a. Give an equation for the magnetic field of the solenoid using the information above, not the derived equation for the magnetic field of an infinite solenoid. b. Draw a top down view of the solenoid and state the symmetry of the solenoid. c. State the direction of the induced electric field everywhere in space. It might help to create an imaginary conducting loop and determine the direction of the current in that loop and recognize that the electric field would drive that current. Also note the symmetry. d. For an arbitrary radius loop inside of the solenoid: Draw your loop on your image of the solenoid above. i. ii. Determine the area of your loop. iii. Give an equation for the magnetic flux through your loop. iv. Use Faraday's law to determine the emf around your loop. v. Use the relationship between the induced emf and the non-Coulomb electric field to determine an equation for the strength of the electric field. vi. Calculate the maximum electric field strength and state where it will occur.
e. For an arbitrary radius loop outside of the solenoid: State how the magnetic field flux changes (if at all), as you increase the radius of your loop. i. ii. Give an equation for the magnetic flux through your loop. iii. Use Faraday's law to determine the emf around your loop. iv. Use the relationship between the induced emf and the non-Coulomb electric field to determine an equation for the strength of the electric field. f. Think about the process you just went through and explain the similarities and differences to using Ampere's law. Ex. Ampere's law involves current density flux, while Faraday's law involves which type of flux?