physique worksheet

Physics 230 Worksheet 13 - Faraday's Law loop inside the center of the solenoid with a radius of 8 cm and a resistance of 1 (1. Find the electromotive force induced within this tiny loop as well as the current running through it as the current of the coil is turned off. |8|=_ I=_ (d)Does the current in the loop run in the same direction as the current of the coil, or the opposite direction? Explain how you know. Direction = (e)The electromotive force is created by an electric field running around the loop, tangent to the wire. Find this electric field's constant magnitude. Also, does this electric field point around the inside of the solenoid in the same direction as the current in the solenoid, or opposite? |E| = _ direction = __ (f) This induced electric field exists, even if the wire loop isn't there! Use your work, above, to find the induced electric field magnitude as a function of radius within the coil. Also, try to describe the direction it moves relative to a cylindrical coordinate system where +z points up and +0 points counterclockwise when looking down to your solenoid from above. |E| = direction = _ Physics 230 Worksheet 13 - Faraday's Law Problem 3 Exploring Faraday's Law For all values of x between 0 and 3w, the magnetic field points out of the paper in the +2 direction and has a uniform and constant magnitude of Bo. For all other values of x, the magnetic field is zero. A square wire loop of size w by w with a resistance R lies within the plane of the paper and is moving to the right, in the +x direction, with a constant speed 12. (a)Draw a figure of this system, labeling the regions of space and their magnetic field vector values, and show the square loop when its front edge is located at x = 0. Also label the velocity arrow of the wire loop. (b)Find the electromotive force induced within the loop for all values of x, where x refers to the location of the front edge of the moving loop. (c) Find the current induced within the wire as a function of x and describe the direction that it is moving. Problem 4 Exploring Faraday's Law Part II, a Challenge Problem We will repeat problem 3, but with a more complicated magnetic field. Assume that between 26 = 0 and x 2 3w, the magnetic field magnitude is instead BO + 3wax axz, and that outside of this region the magnetic field is zero. To solve this problem, you will need to integrate to find an expression for the magnetic flux, and then apply . dCIJ dCDd the chain rule: E X dx dt' Physics 230 Worksheet 13 - Faraday's Law (a)Find the current induced in the wire for values of x between 0 and w, where x refers to the location of the front edge of the wire loop. Which way does this current move around your wire loop? (b) Find the current induced in the wire for values of x between w and 3w, where x refers to the location of the front edge of the wire loop. Which way does this current move around your wire loop? Note there are two answers for direction, take the time to think about it and talk to your classmates. (c) Find the current induced in the wire for values of x between 3w and 4w, where x refers to the location of the front edge of the wire loop. Which way does this current move around your wire loop? Physics 230 Worksheet 13 - Faraday's Law This week we are learning Faraday's Law: how changing magnetic fields can create an emf, and since an emf is a change in electric potential, there must also be an induced electric field. This is a conceptually difficult development that is critically important, since it is the first step in understanding what light is and why it exists. Problem 1 Reviewing some of Faraday's Developments Enter into the table below, the equations described. Motional electromotive force Faraday's Law The integral to calculate magnetic flux The derivative equation showing how flux can depend on changes in the magnetic field or shape of the loop Explain Lenz's Law Problem 2 Considering a Solenoid Consider a solenoid that has a diameter of 10 cm, a length of 1 m and 10,000 turns of the coil. You are currently running 100 amps of current through this wire. The coil is oriented with its central axis along the +2 axis, which points upwards. You put a compass near the top of the coil, and determine that the north end of the compass points downwards. (a)Use what you know about compasses to determine the direction of the magnetic field within the solenoid. 1? points (b)Apply Ampere's Law to find the magnetic field inside the coil. > |B|= (c) Now the current through the wire of the solenoid is turned off at a constant rate over a 0.1 second period. There happens to be a smaller horizontal wire 1