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If [tex]$E^2=C^2 /\left(d^2 Q^2\right)$[/tex] and [tex]$C=100 \times 10^{-6}$[/tex], [tex][tex]$d=1 \times 10^{-6}$[/tex][/tex], and [tex]$Q=100 \times 10^{-6}$[/tex], what is [tex]$E^2$[/tex]?

A. [tex]$4 \times 10^{8}$[/tex]
B. [tex][tex]$8 \times 10^{3}$[/tex][/tex]
C. [tex]$0.12 \times 10^{5}$[/tex]
D. [tex]$44 \times 10^{-7}$[/tex]
E. [tex][tex]$6 \times 10^{77}$[/tex][/tex]



Answer :

GinnyAnswer
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].

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