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A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a certain distance r1 (r1 < R) from the center of the sphere, the electric field has magnitude E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R, the magnitude of the electric field at the same distance r1 from the center would be equal to:

Respuesta :

Answer:

[tex]E' = \frac{E}{8}[/tex]

Explanation:

As we know that that electric field inside the solid non conducting sphere is given as

[tex]\int E.dA = \frac{q_{en}}{\epsilon_0}[/tex]

[tex]\int E.dA = \frac{\frac{Q}{R^3}r_1^3}{\epsilon_0}[/tex]

[tex]E(4\pi r_1^2) = \frac{Qr_1^3}{R^3 \epsilon_0}[/tex]

so electric field is given as

[tex]E = \frac{Qr_1}{4\pi \epsilon_0 R^3}[/tex]

now if another sphere has same charge but twice of radius then the electric field at same position is given as

[tex]E' = \frac{Qr_1}{4\pi \epsilon_0 (2R)^3}[/tex]

so here we have

[tex]E' = \frac{E}{8}[/tex]

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