Law of Induction: What is the value of B in the equation ε = (BA)/t?

In summary, the book and the individual are discussing an equation involving the variables B, A, t, and ε. The individual is confused by the book's method of getting B by itself and points out that it seems to violate basic algebraic rules. The book's solution involves dividing by A and the individual realizes they did not see the slash between A and t, which is hard to see with the modulus sign.
  • #1
bobsmith76
336
0

Homework Statement



See attachment



The Attempt at a Solution



cos theta = 1 so we'll ignore that. I don't understand what's going on, it seems like the book has violated basic algebraic rules.

The original equation, simplified somewhat is:

ε = (BA)/t

In order to get B by itself, you multiply both sides by t

εt = BA

Then divide both sides by A

(εt)/A = B

The book has it differently
 

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  • #2
Right. the book has B = E/(A/t) = Et/A which is what you have.
 
  • #3
Ok, I didn't see that little slash between A and t
 
  • #4
It is a bit hard to see with the modulus sign.
 
  • #5
, with the t in the denominator instead of the numerator. This is mathematically incorrect and would give a different value for B. Can you provide more context or information about where this equation is coming from? It is possible that there is a mistake or typo in the equation, and it would be important to clarify this before proceeding with any calculations or interpretations.
 

FAQ: Law of Induction: What is the value of B in the equation ε = (BA)/t?

What is the Law of Induction?

The Law of Induction, also known as Faraday's Law, states that when a conductor is placed in a changing magnetic field, a current will be induced in the conductor.

What is the difference between mutual and self-induction?

Mutual induction occurs when a changing current in one conductor induces a current in a neighboring conductor, while self-induction occurs when a changing current in a conductor induces a current in the same conductor.

How does the Law of Induction impact the design of electrical devices?

The Law of Induction is the basis for the design of transformers, generators, and other electrical devices that utilize the principle of inducing a current in a conductor through a changing magnetic field.

What factors affect the magnitude of induced current in a conductor?

The magnitude of induced current is affected by the strength of the magnetic field, the velocity of the conductor in the field, and the angle between the conductor and the field.

How is the Law of Induction applied in real-world situations?

The Law of Induction is used in a variety of applications, such as power generation, wireless charging, and electromagnetic induction cooktops. It is also used in the production of electricity from renewable sources, such as wind and hydroelectric power.

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