-ve sign in expression of induced emf

[abhineetK]

-ve sign in expression of "induced emf"

What is the concept behind putting negative sign in:
e=-[rate of change of flux]
Which direction does it signify??
How does direction affect the equation?
How and where can we use negative sign in other expressions of induced emf??

 

[Feldoh]

The negative sign basically signifies Lenz's Law which tells you something about the direction of the induced emf.

 

[sophiecentaur]

Lenz's Law says it's "such as to oppose its cause", as they told me in School. It's a reaction, in the same way as an object pushes back at you when you try to move it. The negative sign makes the sums come out right.

 

[abhineetK]

We see that the fact whether the current increases or decreases too affect the equation by making the induced emf -ve or +ve respectively.
How should we assign -/+ signs to current and magnetic field depending on their direction?
Is their any convention or any concept?

 

[cabraham]

Think about it if the negative sign was not there. Then, the induced emf/mmf/flux/torque/speed, would be in the same direction as the existing quantity.

A motor is switched on, and the current is great. As the motor picks up speed, the induced current & voltage (mmf/emf) both increase. But the -ve sign, an artifact of Lenz' law, describes the induced quantities as oriented in a direction opposite to the original quantities. Hence the overall current drawn from the power source decreases since the induced current opposes the original.

Otherwise, it would increase, generating more flux, and yet more emf/mmf, yet more current, etc. Power would increase without bound and energy would be created out of thin air.

Lenz' law also covers mechanical quantities like torque and speed. If you pedal a bicycle type generator with no load, you reach a speed of let's say 300 rpm. Now add a significant load, 50 watts. The slight torque you applied pedaling under no load is now opposed by a counter torque due to the induction. When the load current is introduced, it generates a torque whose orientation is opposite to your pedaling torque. Otherwise the speed would keep increasing, with energy being created. In order to preserve the same 300 rpm speed (and the same voltage), you must increase your pedal torque so as to counter the counter torque. So an increase in electrical output power mandates a corresponding increase in mechanical input power.

Does this make sense?

Claude