• abhineetK
In summary: Shannon's communication theory used a mathematical technique called indeterminacy to describe information in a communication system. In order to send a clear signal, the sender must be certain about the state of the receiver at the time the signal is being sent. Unfortunately, this is not always possible. For example, consider two people trying to communicate over a noisy channel. The sender sends a message, but the receiver can't tell whether it was received. The receiver could try to retransmit the message, but this would waste bandwidth and time. Or the receiver could just give up and stop trying to receive the message. In summary, Claude Shannon's communication theory uses indeterminacy to describe how a sender can't be
abhineetK

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??

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

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.

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?

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

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## 1. What does the negative sign in the expression of induced emf represent?

The negative sign in the expression of induced emf represents the direction of the induced current. It indicates that the induced current flows in the opposite direction of the change in magnetic flux.

## 2. Why is the negative sign used in Faraday's law of induction?

The negative sign is used in Faraday's law of induction to show the relationship between the change in magnetic flux and the induced emf. The negative sign indicates that the induced emf is directly proportional to the rate of change of magnetic flux but is in the opposite direction.

## 3. What happens if the negative sign is not included in the expression of induced emf?

If the negative sign is not included in the expression of induced emf, it would indicate that the induced current flows in the same direction as the change in magnetic flux. This would be incorrect as the direction of the induced current is always in the opposite direction.

## 4. How does the negative sign affect the magnitude of the induced emf?

The negative sign does not affect the magnitude of the induced emf. It only indicates the direction of the induced current. The magnitude of the induced emf is determined by the rate of change of magnetic flux.

## 5. Can there be a positive induced emf in a circuit?

Yes, there can be a positive induced emf in a circuit. This would occur if the change in magnetic flux and the induced current are in the same direction. However, the negative sign in the expression of induced emf would still be used to indicate the direction of the induced current.

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