To find [tex]\( E^2 \)[/tex] given the formula:
[tex]\[
E^2 = \frac{C^2}{d^2 Q^2}
\][/tex]
where the given values are:
- [tex]\( C = 100 \times 10^{-6} \)[/tex]
- [tex]\( d = 1 \times 10^{-6} \)[/tex]
- [tex]\( Q = 100 \times 10^{-6} \)[/tex]
Let's break down the steps to calculate [tex]\( E^2 \)[/tex]:
1. Square the given values:
[tex]\[
C^2 = (100 \times 10^{-6})^2 = 10^4 \times (10^{-6})^2 = 10^4 \times 10^{-12} = 10^{-8}
\][/tex]
[tex]\[
d^2 = (1 \times 10^{-6})^2 = 10^{-12}
\][/tex]
[tex]\[
Q^2 = (100 \times 10^{-6})^2 = 10^4 \times (10^{-6})^2 = 10^4 \times 10^{-12} = 10^{-8}
\][/tex]
2. Calculate the denominator:
[tex]\[
d^2 Q^2 = 10^{-12} \times 10^{-8} = 10^{-20}
\][/tex]
3. Substitute the squared values into the formula and simplify:
[tex]\[
E^2 = \frac{C^2}{d^2 Q^2} = \frac{10^{-8}}{10^{-20}} = 10^{-8 - (-20)} = 10^{-8 + 20} = 10^{12}
\][/tex]
Therefore, the value of [tex]\( E^2 \)[/tex] is:
[tex]\[
10^{12} = 1000000000000.0
\][/tex]
So, the correct answer is not among the provided options, but the value of [tex]\( E^2 \)[/tex] is [tex]\( 1000000000000.0 \)[/tex].
