College

The electric potential in a particular region of space varies only as a function of y-position and is given by the function:

\[ V(y) = 1.69y^2 + 15.6y + 52.5 \, \text{Volts} \]

Calculate the magnitude of the electric field at the position \( y = 22.5 \) meters.

Answer :

Answer:

[tex]E = 55.9583\ Volts/meter[/tex]

Explanation:

First let's find the electric potential using y = 22.5:

[tex]V(y) = 1.69y^2 +15.6y+52.5[/tex]

[tex]V(22.5) = 1.69(22.5)^2 + 15.6*22.5 + 52.5[/tex]

[tex]V(22.5) = 1259.0625\ Volts[/tex]

Then, to find the magnitude of the electric field, we just need to divide the electric potential by the distance y:

[tex]E = V/d[/tex]

[tex]E = 1259.0625/22.5[/tex]

[tex]E = 55.9583\ Volts/meter[/tex]

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