EMF Induced in a Moving Conductor (“Motional EMF”) Figure 29-12a. A conducting rod is moved to the right on a U-shaped conductor in a uniform magnetic field B that points out of the page. The induced current is clockwise.

This figure shows another way the magnetic flux can change. It can change if a conducting loop is moved in a static magnetic field. Figure 29-12a. A conducting rod is moved to the right on a U-shaped conductor in a uniform magnetic field B that points out of the page. The induced current is clockwise.

It takes an external force to keep it moving. The induced current in the figure is in a direction that tends to slow the moving bar. That is, It takes an external force to keep it moving. Figure 29-12b. Upward force on an electron in the metal rod (moving to the right) due to B pointing out of the page.

holds ONLY if B, l, & v are mutually perpendicular. The induced emf has magnitude = B[(A)/(t)] = Bℓ(x)/(t) = Bℓv This holds ONLY if B, l, & v are mutually perpendicular. If they are not, then it is true for their perpendicular components.

Does a moving plane develop a large emf? Induced emf magnitude: Example: Does a moving plane develop a large emf? A plane travels at speed v = 1000 km/h in a region where Earth’s magnetic field B = 5  10-5 T & is nearly vertical. Calculate the potential difference induced between the wing tips that are l = 70 m apart. Solution:  = B l v  1 V

Motional emf Electrons in the conductor experience a Motional emf is the emf induced in a conductor moving through a constant magnetic field. Electrons in the conductor experience a force that is directed along ℓ: .

qE = qvB or E = vB. This charge separation produces an This force causes electrons move to the lower end of the conductor & accumulate. This charge separation produces an electric field inside the conductor. The charges accumulate at both ends of the conductor until they are at steady state. When that happens, qE = qvB or E = vB.

This charge separation produces an electric field inside the conductor. qE = qvB or E = vB. This electric field is related to the potential difference across the ends of the conductor: V = E ℓ =B ℓ v. This V is maintained between the ends of the conductor as long as it continues to move through the uniform B field. If the direction of the motion is reversed, the polarity of the V is also reversed.

Example: Force on a conducting bar. To make the bar move to the right at speed v, you need to apply an external force on the bar to the right. Calculate (a) The magnitude of the required force. (b) The external power needed to move the rod. Solution: a. The external force needs to be equal and opposite to the magnetic force (IlB) if the rod is to move at a constant speed. I = Blv/R, so F = B2l2v/R. b. The external power is Fv = B2l2v2/R, which is equal to the power dissipated in the resistance of the rod (I2R).

Sliding Conducting Bar The induced emf is The resistance in the circuit is R, so the current is

Sliding Conducting Bar The applied force does work on the bar. It moves the charges through a magnetic field & induces a current. The change in energy of the system during some time interval must be equal to the transfer of energy into the system by work. The power input is equal to the rate at which energy is delivered to the resistor.

Lenz’s Law: More on Lenz’s Law Faraday’s Law says that the induced emf & the change in magnetic flux have opposite algebraic signs. This has a physical interpretation known as Lenz’s Law: The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop. The induced current tends be in a direction so to keep the original magnetic flux through the circuit from changing.

Lenz’ Law, Example The induced current must produce a magnetic The conducting bar slides on the two fixed conducting rails. The magnetic flux due to the external magnetic field through the enclosed area increases with time. The induced current must produce a magnetic field out of the page. So, the induced current must be counterclockwise If the bar moves in the opposite direction, the direction of the induced current will also be reversed.