Respuesta :
Answer:
Distance from the line with the field strength of 2000N/C = 0.7071 D or D√(0.5) or D/(√2)
Explanation:
Electric field is given by,
E = kQ/r²
where k = constant, Q = total charges, R = distance from the line of charge = D
Provided, total charges are constant, then,
The electric field is inversely proportional to the square of D.
E ∝1/D²
E = c/D²
c represents kQ, the two constant parameters.
1000 = c/D²
c = 1000D²
For E = 2000 N/C
Let the distance from the line with that field strength be x
E = kQ/x²
E ∝1/x²
E = c/x²
2000 = c/x²
c = 1000D²
2000 = 1000D²/x²
x² = 0.5D²
x = √(0.5D²)
x = D√0.5
x = 0.7071 D or D√(0.5) or D/(√2)
Hope this Helps!!!
When charge is constant the field strength is inversely proportional to the square root of distance. The distance from the line is [tex]d\sqrt{0.5}[/tex] when field strength is 2000 N/C.
From electric field,
[tex]E = \dfrac {kQ}{r^2}[/tex]
where
[tex]k[/tex] = constant,
[tex]Q[/tex]= total charges,
[tex]r[/tex] = distance from the line of charge = [tex]D[/tex]
Since the charge is constant,
[tex]E = \dfrac{c}{x^2}[/tex]
[tex]c[/tex] represents constant [tex]kQ[/tex],
[tex]1000 = \dfrac{c}{D^2}[/tex]
[tex]c = 1000D^2[/tex]
For [tex]E = 2000 \rm\ N/C[/tex]
[tex]2000 =\dfrac {c}{x^2}[/tex]
Put the value of
[tex]2000 = \dfrac{1000D^2}{x^2}\\\\x^2= 0.5D^2\\\\x = d\sqrt{0.5}[/tex]
Therefore, the distance from the line is [tex]d\sqrt{0.5}[/tex] when field strength is 2000 N/C.
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