In many cases, the effect of an electromagnetic interaction is perpendicular to its cause. Describe two different examples that illustrate this.

Short Answer

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Question: Give two examples that illustrate the concept that the effect of an electromagnetic interaction is often perpendicular to its cause. Answer: One example is the magnetic force on a moving charge, in which the force acts perpendicular to both the magnetic field and the velocity of the charge. Another example is the electromotive force in a conductor moving through a magnetic field, where the induced EMF creates a Lorentz force that is also perpendicular to the length of the conductor and the magnetic field.

Step by step solution

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Example 1: The magnetic force on a moving charge

In this situation, a charged particle moves through a magnetic field. The force acting on the charge as it moves through the field is perpendicular to both the direction of the magnetic field and the velocity of the charge. This is due to the fact that the magnetic force on a moving charge is given by the equation: $$\vec{F} = q(\vec{v} \times \vec{B})$$ Where $$\vec{F}$$ is the magnetic force, $$q$$ is the charge, $$\vec{v}$$ is the velocity, and $$\vec{B}$$ is the magnetic field. Since the force is the cross product of the velocity and the magnetic field, it is perpendicular to both.
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Example 2: The electromotive force in a conductor moving through a magnetic field

When a conducting wire moves through a magnetic field with a perpendicular velocity to the magnetic field lines, an electromotive force (EMF) is induced in the wire. This is due to Faraday's law of electromagnetic induction, which states that the induced EMF is equal to the negative rate of change of the magnetic flux through the closed loop of the wire: $$\epsilon = -\frac{d\Phi}{dt}$$ The presence of the induced EMF in the wire can cause a current to flow in a closed loop, which also experiences a force known as the Lorentz force. The Lorentz force is given by the equation: $$\vec{F} = I(\vec{l} \times \vec{B})$$ Where $$\vec{F}$$ is the Lorentz force, $$I$$ is the current, $$\vec{l}$$ is the length of the conductor, and $$\vec{B}$$ is the magnetic field. Again, since the force is the cross product of the length of the conductor and the magnetic field, it is perpendicular to both.

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