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Terminal Speed expression

  • #1

Homework Statement


29-59_zpsca4d2d1f.png



Homework Equations


That is the solution:
29-59_zps10e24f3f.png



The Attempt at a Solution


I think ε≠Bvl because ε = - dø/dt=- Bd(v.t)/dt, v is not constant.
Why ε=Bvl???
 

Answers and Replies

  • #2
CAF123
Gold Member
2,889
88
The induced emf in the loop is related to the change in flux through a surface whose boundary is the loop: $$\epsilon = -\frac{\text{d} \phi}{\text{d}t} = -\frac{\text{d}}{\text{d}t} \int_S \mathbf{B} \cdot \mathbf{dS}$$
In your case, the B field is of constant magnitude and direction and dS instantaneously is Ldx.
 
  • #3
1,948
200
dø/dt = d(B. Area)/dt = d(BLx)/dt = BL dx/dt = BLv.
 

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