A solid insulating sphere has total charge Q and radius R. The sphere's charge is distributed uniformly throughout its volume. Let r be the radial distance measured from the center of the sphere. If E = 520 N/C at r= R/4, what is E at r = 4R?

2.03N/C

Explanation:

Electric field, E, is given as:

E = kQ/r²

When r = R/4, E = 520N/C.

=> 520 = kQ/(R/4)²

520 = 16kQ/R²

=> R² = 16kQ/520 (1)

When r = 4R,

E = kQ/(4R)²

E = kQ/16R²

=> R² = kQ/16E (2)

Equating (1) & (2):

16kQ/520 = kQ/16E

=> E = 520/(16 * 16)

E = 520/256

E = 2.03 N/C

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

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