Electromagnetic Induction
Induced Currents We learned that a current can create a magnetic field Michael Faraday proved that a changing a magnetic field can induced (create) a current in a circuit (or loop/coil)
Induced Currents Current is induced when field lines are cut. The coil moves perpendicular to the field Current is not induced when the coil of wire moves parallel to the field
Induced Emf The current flows in the coil because the change in the magnetic field strength (increasing or decreasing) causes a voltage (Emf Ɛ). The charges in the coil will resist moving There is a relationship between the current, the resistance, and the induced voltage V = IR (Ohm s Law) *Ɛ can be substituted for V
Factors affecting induced Emf 1. The speed of a conducting rod of length L as it moves with velocity v through a magnetic field B Ɛ = vbl *Magnetic force will always oppose the motion Use RHR to determine the direction of the current (your thumb) which is also towards the positive end of the rod An external force equal to the magnetic force but opposite in direction must be applied to the rod to keep it in motion
Factors affecting induced Emf 2. The change in the number of field lines in a going through the coil in a magnetic field This occurs by either increasing or decreasing the area of the magnetic field
Factors affecting induced Emf Or increasing or decreasing the strength of the magnetic field
Lenz s Law Ultimately, the amount of field that goes through a coil/loop depends on two things: the strength of the field and the area of the loop. This is called Magnetic Flux Unit: Weber (Wb) or T m 2 Current is induced in a coil/loop when the magnetic flux changes (Lenz s Law)
Lenz s Law Lenz s law tells us to look for situations where the flux is changing. This can happen in Three ways: 1. The magnetic field through the loop increases or decreases 2. The loop changes area or angle 3. The loop moves into or out of a magnetic field
Using Lenz s Law to determine the direction of the induced current 1. Determine the direction of the applied magnetic field 2. Determine how the flux is changing inside the coil/loop 3. Determine the direction of the induced magnetic field that will oppose the change in the flux - Increasing flux: the induced magnetic field will be in the direction opposite of the applied magnetic field trying to decrease the flux - Decreasing flux the induced magnetic field will be in the same direction as the magnetic field trying to increase the flux 4. Use RHR to determine the current direction in the loop that generates the induced magnetic field found in step 3
Faraday s Law An emf (Ɛ) is induced in a conducting loop is the magnetic flux through the loop changes. Ɛ = Δɸ Δt Δɸ = ɸ f - ɸ i
Example: A potential difference of 0.050 V is developed across the 10 cm long wire as it moves through a magnetic field at 5.0 m/s. What are the direction and strength of the magnetic field?
The figure shows a 15 cm long metal rod being pulled along two frictionless, conducting rails at a constant speed of 3.5 m/s. The rod has a resistance of 0.65Ω. (a) what is the current induced in the rod? (b) What force is required to keep the rod moving at a constant speed?
Example: The plastic cart shown moves with negligible friction on a horizontal surface. Attached to the cart is a rigid rectangular loop of wire that is 0.10 m by 0.20 m and has a resistance of 4.0 Ω. A uniform magnetic field of 2.0 T, perpendicular to and directed into the plane of the page, starts at x = 0, as shown. (a) On the figure below indicate the direction of the induced current in the loop when its front edge is at x = 0.12 m. Justify your answer (b) When the front edge of the rectangular loop is at x =0.12 m, its speed is 3.0 m/s. Calculate the following for that instant. i. The magnitude of the induced current in the loop of wire ii. The magnitude of the net force on the loop