Question

A solenoid has 450 loops, each of radius 0.0254 m. The field increases from 0T to 3.00 T in a certain amount of time. If 15.6 V of EMF are generated in the coil, how much time elapsed? (Hint: What is the area of a circle?) (Unit = s)

Answer 1

0.175s

Step-by-step explanation:

To find the time elapsed you use the following formula:

`emf=-N(d\Phi)/(dt)=-N(d(AB))/(dt)`

N: turns

A: cross area of the loop

B: magnitude of the magnetic field

for discrete changes and for a constant area A you have:

`emf=-N(\pi r^2)(\Delta B)/(\Delta t)`

You replace the values of the parameters to calculate the elapsed time:

`\Delta t=-N((\pi r^2)\Delta B)/(emf)\\\\\Delta t=-(450)((\pi(0.0254m)^2)(3.00T-0.00T))/(15.6V)\\\\\Delta t=0.175s`

hence, the elapsed time is 0.175s