Why Is Cosine Used to Calculate Induced Voltage in a Conductor?

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SUMMARY

The discussion centers on the use of the cosine function to calculate induced voltage in a conductor placed within an electric field. When the conductor aligns with the electric field, the induced voltage is maximized at E·l. The angle θ between the electric field and the conductor determines the effective voltage, calculated as E·cos(θ)·l. This approach emphasizes that cosine represents the projection of the electric field vector along the conductor, while sine would apply to components perpendicular to it, which are less relevant in this context.

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  • Understanding of basic trigonometry, specifically sine and cosine functions.
  • Familiarity with electric fields and their properties.
  • Knowledge of induced voltage concepts in conductors.
  • Basic comprehension of vector projections in physics.
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  • Study the principles of vector projections in physics.
  • Learn about electric fields and their effects on conductors.
  • Explore the relationship between angle and induced voltage in electromagnetic theory.
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This discussion is beneficial for physics students, electrical engineering students, and anyone interested in understanding the principles of induced voltage and the application of trigonometry in electrical contexts.

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http://www.berkeleyscience.com/maxwells.htm

"""""When a conductor (a wire) is placed in an electric field, the field may induce a voltage in the conductor. The diagram shows an electric field in the x direction with magnitude E. If the conductor is perpendicular to the E field, there is no induced voltage. If the conductor is aligned with the E field, the induced voltage is E·l where l is the length of the wire. If the angle between the E field and the wire is θ then the induced voltage is E·cos(θ)·l."""

^^ this is quoted from the link i just gave ^^
It is with reference to this image here : http://www.berkeleyscience.com/images/efield.jpg

Now I am curious why Cos is used when determining the induced voltage, that's all i am curious about. Why not Sin? How would you determine to use Cos? Please can you help me in laymans terms because I am only beginning Trig properly
 
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The maximum voltage is induced when the E-field vector points along the conductor. When the E-field is at some angle, then it is the 'projection' or component of the E-field vector parallel to the conductor that causes the voltage.

Think about - what is the significance of the cos and the angle between the hypotenuse and one leg.
http://hyperphysics.phy-astr.gsu.edu/hbase/ttrig.html

If one was interested in the projection or component of the E-field in the transverse direction to the conductor, then one would used the sin. But the transverse E-field would not be so significant here, although it would produce a tranverse voltage across the conductor, as a opposed to along the conductor.
 

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