Download 20.3 Motional emf

20.3 Motional emf Consider the following situation. A conducting rod is moving to the right with a speed v in a magnetic field region directed into the page. The free electrons in the conductor are subjected to a magnetic force directed downwards and equals 𝐹 = 𝑞𝑣𝐵 So the electrons will move downwards leaving a positively charged region upwards and making a negatively charged region at the bottom. So an electric field directed downwards is induced When the magnetic force becomes equal to the electric force on a free electron, its motion stop and an induced emf is formed. From previous lessons ℰ = 𝐸𝑙 Now 𝐹! = 𝐹! 𝑞𝐸 = 𝑞𝑣𝐵 𝑞ℰ
= 𝑞𝑣𝐵 𝑙
ℰ = 𝑣𝐵𝑙 𝑜𝑟 Δ𝑉 = 𝑣𝐵𝑙 This emf is called the motional emf because it is due to the motion of a conductor in a magnetic field Example: Consider a conducting rod moving along two conducting rails to the right with a speed v forming a closed loop. The system is placed in a magnetic field region as shown in the figure This is the same answer that we got for the motional emf as it must be. Moreover the current must flow CCW. If the resistance of the circuit is R, then