# [物理]Motional emf諗唔明

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The explanation given in your physics textbook is quite misleading (but unfortunately, most local physics textbooks use such explanation).

Induced emf on the moving rod is produced when the rod cuts through magnetic field lines. The reason behind is that the charge carriers (which are electrons in the case of a metal rod) inside the rod interact with the magnetic field. Such interaction gives rise to a force (known as Lorentz force) that propels the electrons to move along the rod in a certain direction. This is how induced emf (or induced current) is produced.

Faraday discovered that the magnitude of the induced emf is proportional to the number of field lines cut by the rod in a unit time, which (for reason given below) he described it as the "rate of change of magnetic flux" . This is Faraday's Law of electromagentic induction.

Because the number of field lines cannot be physically counted, the term "magntic flux" is used instead in physics. Therefore, the concept of "rate of change of magnetic flux" can be interpreted as "the number of magnetic field lines being cut ( by the moving rod) in a unit time".

When the rod moves faster, either to the left or right, the number of field lines cut in a unit time would increase. This indicates a higher induced emf produced on the rod.

In the actual fact, in classical electromagnetism, electric or magnetic fields are based on the concept of "field lines".

2013-07-21 16:46:31 補充：

Q:通過metal rod既magnetic field lines既總數唔係應該不變咩?

A: I think you still cannot grasp the concept of electromagnetic induction.

Induced emf occurs is not because of the field lines that pass through the rod, but due to the MOTION of the rod that CUTS through few lines.

2013-07-21 16:56:02 補充：

As word limit is reached, continue on [意見] section.

2013-07-21 16:57:19 補充：

Q:...本書就話冇induced emf,點解個結果會同metal rod果個唔同既?

A: Your book is wrong. There is indeed emf produced, but no induced current.

Because of the motion of the rectangle, the two sides of the rectangle,that are perpendicular to the field lines,are SEPARATELY CUTTING through magnetic field lines...

2013-07-21 16:58:14 補充：

(cont'd)..Hence,emf are induced on each of the 2 sides of the rectangle. Using Fleming's Right hand Rule, you would find that these two induced emf are in the same direction, thus tends to drive current opposing each other. Resulting in no current at all...

2013-07-21 16:59:14 補充：

(cont'd)...This situation is similar to two cells connected in parallel to form a closed circuit. There are emfs but no current could be delivered.

2013-07-21 17:01:32 補充：

typo correction, last sentence "... CUTS through field lines"

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• Motional And Emotional 23

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Mo ti o na land de mo ti o na le

資料來源： Way Answer You Bi Putonghua
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• The force acting on a charge particle by an electromagnetic field is given by

F = q ( E + v x B ), [or in Gaussian units F = q ( E + (v/c) x B ), c = speed of light]

where q is the charge of the particle, E and B are the electric and magnetic field which are 3 dimensional vectors, v is the velocity vector of the particle, and x is the cross product of vectors.

The emf is given by the energy gained (or lost) for a unit of charge to move once around a loop. In math terms, emf = line integral of (F/q) along the loop. This gives the units of electric potential: (F/q)L ~ EL ~ V, for length L and potential V.

There are two factor giving rise to a non-zero emf. (1) Change of the area of the loop, and (2) change of local magnetic field B inside the loop. Both leads to a change of magnetic flux across the loop, the sum (or surface integral) of magnetic field over an area bounded by the loop.

These can be separately understood. (1) A change in the area of the loop requires the metallic line to cross magnetic field. This gives rise to the Lorentz force q v x B, as the wire is moving in velocity v. The emf is the sum over all the forces along the whole loop. This would be zero if the loop just move pass a uniform B-field without changing area because forces overall cancel. So the Lorentz force can give rise to a non-zero emf only if (a) the loop changes area, or (b) it moves pass a spatially non-uniform B-field.

(2) The other component of force is q E, and the electric field can be generated by a temporally changing B-field by the Faradays law, curl(E) = - dB/dt, or equivalently

line integral of E along the loop = - d(magnetic flux across loop)/dt

Thus a time changing B-field also gives rise to emf.

In general, (1) + (2) is responsible to the total emf around the loop.

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• 簡單d既其實應該分做兩種來考慮的

首先係1d係field入面無中間空左既area既野(rod)

你需要知道個定義係當conductor cut through field lines/field lines change(field強度/角度)既時候就會有induced emf，e個已經說明左單單一枝metal rod點解會有induced emf

姐係係入面移動已經有emf 啦 ，你最好記住

然後係1d係field入面有中間空左既area既野(coil)

簡單d來諗，就係要當中個area有變/field強度or角度有變先會有flux change，例如當個coil moving out個field咁

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