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Q Q’ e Move charge Q to position Q’ creates propagating ‘kink’ in the electric field, which affects the motion of electron e.

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The electric field and the magnetic field in an electromagnetic wave are perpendicular to each other and to the direction of propagation of the wave What do the electric field lines of an electromagnetic wave look like?

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We know that an electromagnetic wave carries energy, because it can causes charges to accelerate as it passes by them. If it gives kinetic energy to these “absorbers” or “receivers” then energy must be lost by the wave. If electromagnetic waves contain energy, it also follows that the source of the wave, the charged matter which made the original disturbance in the field, must lose energy. This usually means it loses kinetic energy, so its motion decreases, or is “damped.” What form does the energy carried by the wave take? Obviously it is partly electric field energy and partly magnetic field energy.

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The density of electric field energy (i.e. the field energy per unit volume of space) contained in an electric field of strength E is U e = ½ E 2. Similarly the density of magnetic field energy contained in a magnetic field of strength B is U m = ½ B 2 / . You can calculate each of these formulae for the specific cases of a capacitor (electric) and an inductor (magnetic), as was done in previous chapters, but it is also true for any electric or magnetic field, including an electromagnetic wave.

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Now we made the claim earlier that you can’t have just an electric wave or just a magnetic wave. The only thing keeping the magnetic field in the wave from disappearing is that the electric field is constantly changing. The only thing keeping the electric field from disappearing is that the magnetic field is constantly changing. Given this, which of the two fields is stronger? There is a surprisingly strong rule in physics that if energy has the choice of going into two or more forms, that it will choose between them equally. So it is not surprising that the magnetic and electric field energy densities in an electromagnetic wave are always equal to each other.

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So we have that U e = ½ E 2 = U m = ½ B 2 / . What does this tell us about the relative strengths of E, the electric field of the wave, and B, the magnetic field of the wave? a)E = B b)E = B / c)E = B/( ) 1/2 d)E = B/

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Correct answer: C So we have the interesting result that E/B = 1/( ) 1/2 But what does this mean? The units of are C 2 /(N m 2 ) The units of are T m/A Keeping in mind that the force on a moving charged particle is F = q (v x B), which of the following is correct for the units of 1/( ) 1/2 ? a)m b)m/s c)T C/s d)N A

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Correct answer: B So this funny looking quantity, which is equal to the ratio between the electric and magnetic field strengths of an electromagnetic field, is a velocity. Since it is the tugging of each field on the other which keeps the wave going, it is rather like the tension in water waves or waves on strings that determines the speed of the wave. So if this is the speed of an electromagnetic wave, how fast is it? = 1.26 x T m/A and = 8.85 x C 2 /(N m 2 ) The answer is that 1/( ) 1/2 = 3 x 10 8 m/s = c the speed of light

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The person who realised this was James Clerk Maxwell ( ) a Scottish theoretical physicist who was a contemporary of Faraday. Unlike Faraday he came from a very wealthy background and was very well educated. But he thought in a similar way and seized on Faraday’s experimental results and on his way of thinking about the electric and magnetic fields to produce a set of equations, known as Maxwell’s equations, which described the behavior of both fields. Because the two fields were mixed together in the equations people began to speak of the Electromagnetic field.

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Maxwell quickly realized that he could combine his equations together to create a wave equation, the type of equation which described waves on strings, in water or in air. But in this case the wave would exist only in the electromagnetic field. All wave equations contain a factor which is the velocity of the wave and in Maxwell’s calculation this worked out to be 1/( ) 1/2. When he calculated this number and found it was the same as the speed of light he realized he had discovered the true nature of light itself, it was simply a kind of electromagnetic wave.

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The Intensity of an electromagnetic wave is the amount of energy it delivers to a unit area per unit time. So we define it as I = U/(A t) = u V/(A t) Where I is the intensity and u is the energy density in the wave. Which of the following is the correct expression for I? a)I = u c b)I = u/c c)I = u A d)I = u

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Correct answer – A First of all, it has the right units. Also I = U/(A t) = u V/(A t) = u c A t /(A t) = u c So the intensity is simply the energy density in the wave times the speed with which the wave is carrying that energy to you. But how do receivers or absorbers actually absorb the energy? Usually by the fact that the electric and magnetic field vectors in the wave impart a force on the particles in the receiver and make them move, thus giving them kinetic energy.

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D E B +e Suppose you have an proton +e upon which an electromagnetic wave impinges. The direction of propagation of the wave (labelledD), and the directions of the electric (E) and magnetic fields (B) are as shown. Which direction will the force exerted on the proton by the magnetic field point (assuming the proton is not moving at all when the wave first reaches it)? a)E b)B c)Opposite to D d)D

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Correct answer – D To begin with the electron isn’t moving, but as the electric field operates upon it, it will begin to move along the electric field line in the direction of its arrow, so in the direction E. Once it is moving the magnetic field can affect it, according to the equation which gives the magnetic force exerted on the proton by the wave F = q v x B. If v is in the direction of E then v x B, by the right hand rule, will be in the direction of D. v B F

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What this means is that electromagnetic fields exert a force on charged particles which causes them to recoil when hit. So it gives them some momentum in the direction of the wave. This momentum has to come from somewhere. Where can it have come from? a)Empty space b)The particle which was the source of the wave c)The previous particle the wave struck d)It came into existence from nowhere

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Correct answer – B Just as the receiver recoils when the wave hits it, so the source of the wave must recoil when it emits it. If the wave goes off in one direction the source recoils in the other direction, just as a cannon does when it fires off a cannonball. So electromagnetic waves carry momentum from the source to the receiver. The amount of momentum carried by an electromagnetic wave is a simple formula p = E/c = U/c where U or E is the amount of energy in the wave. As we shall see later on, it is from this formula that Einstein derived his famous equation E = m c 2.

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