Find the inductance and induced emf for a solenoid with a cross sectional area of 1.3*10^-3m^2. The solenoid, which is 9.0cm long is made from a piece of wire that is 44m in length. Assume that the rate of change is 7.14A/s.

Can someone explain how to solve this? I know the answers are L=2.2mH and E = 0.016V

Question

Find the inductance and induced emf for a solenoid with a cross sectional area of 1.3*10^-3m^2. The solenoid, which is 9.0cm long is made from a piece of wire that is 44m in length. Assume that the rate of change is 7.14A/s.

Can someone explain how to solve this? I know the answers are L=2.2mH and E = 0.016V

gudden · Answer

Since, in case of self induction, an isolated coil too produces emf when its subjected  to the change in ( magnetic ) flux due to the varying current flowing through the same wire.

i.e. $$\phi = L I$$  - (1)

where phi represents ' flux linkage'

we know magnitude of the emf is the rate of change of ( magnetic) flux through the circuit.
i.e.
$$emf = - \frac{ d \phi }{ dt }$$ - (2)

using 1 in 2

we get

$$emf = - L \frac{ dI }{dt }$$


Hopefully that helps, I urge you to try to solve the question if possible, else am there to help :)

radar · Answer

I hope you study text provides an equation to calculate the inductance with the information provided.  The information provided will allow you to calculate the coil diameter, the number of turns.  You have been provided the area of the coil, the length of the coil, the length of wire.  Some things you may have to assume:  air core, diameter of the wire (in order to determine if it is a single layer winding or multilayer winding,