# Why Cos is used here

1. Jun 20, 2009

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

2. Jun 20, 2009

### Staff: Mentor

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.