Question

A solid sphere of radius 40.0cm has a total positive charge of 26.0μC uniformly distributed throughout its volume. Calculate the magnitude of the electric field(b) 10.0cm

Answer 1

The magnitude of the electric field is 3.65×10^5N/C directed radially outward.

R (radius of the solid sphere) = (10cm)( 1m /100cm) = 0.1m

$Q\;(\text{total charge of the solid sphere})=(26\;\mathrm{\mu C})\left(\dfrac{1\;\mathrm{C}}{10^6\;\mathrm{\mu C}} \right)=\textcolor{#ff9c8c}{26\times 10^{-6}\;\mathrm{C}}$

Since ${r=0.1\;\mathrm{m} < R}$, we can use Equation $E&=\dfrac{Qr}{4\pi \epsilon_0 R^3}\tag{5}$ to find the magnitude of the electric field:

Substitute numerical values:

$E&=\dfrac{(26\times 10^{-6})(0.1)}{4\pi (8.8542\times 10^{-12})(0.4)^3}\\ &={3.65\times 10^5\;\mathrm{N/C}\;\text{directed radially outward}}}$

Magnitude generally refers to distance or quantity. In comparison to motion, Magnitude defines the size of an entity or its speed when moving.

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