Respuesta :
Answer:
The value is [tex]E_1 = 49224.1 \ N/C [/tex]
Explanation:
From the question we are told that
The radius is [tex]r = 13 \ cm = 0.13 \ m[/tex]
The electric field is [tex]E = 78400 \ N/C[/tex] at a distance [tex]d = 7.5 \ cm = 0.075 \ m[/tex]
Generally the electric field at a distance [tex]d = 7.5 \ cm = 0.075 \ m[/tex] is mathematically represented as
[tex]E = \frac{k * q * d}{r^3}[/tex] Note: the reason we are using this
formula is because [tex]d < r[/tex]
Here k is the coulomb constant with value [tex]k = 9*10^{9}\ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}.[/tex]
=> [tex]78400= \frac{9*10^{9} * q * 0.075}{0.13^3 }[/tex]
Generally the electric field at a distance [tex]d = 21.6 \ cm = 0.216 \ m[/tex] is mathematically represented as
[tex]E_1 = \frac{k * q }{^2}[/tex] Note: the reason we are using this
formula is because [tex]d > r[/tex]
Now dividing [tex]E_1\ \ by \ \ E[/tex]
[tex]\frac{E_1}{78400} = \frac{\frac{9*10^9 * q}{0.216^2} }{\frac{9*10^9 * q * 0.075}{0.13^3} }[/tex]
=> [tex]E_1 = \frac{0.13 ^3}{ 0.075 * 0.216^2} * 78400[/tex]
=> [tex]E_1 = 49224.1 \ J [/tex]