Question

A sphere with radius 1cm has a charge of 5x10^-9C spread out uniformly over its surface. What is the magnitude of the electric field due to the sphere at a location 4 cm from the center of the sphere?

Short answer

The magnitude of the electric field due to the sphere at a location 4cm from the center of the sphere is $2.81\times {10}^{4}N/C$ .

Step-by-step solution

Identification of the given data

The given data can be listed below as

• The radius of a sphere is: R = 1 cm .
• The electric charge on the sphere is: q = 5x10^-9C .
• The distance of a location from the center of the sphere is: r = 4cm .

Significance of electric field

The electric field due to a specific charge that lies on a surface of a particular body at a location out from the body would have non-zero values. The electric field has a direct linear relationship with the electric charge.

Determination of the magnitude of the electric field due to the sphere at a location 4cm from the center of the sphere.

The expression of the magnitude of the electric field outside the sphere can be expressed as:

$E=k\left(\frac{q}{r^2}\right)$

Here, E represents the electric field due to the sphere at a location 4cm from the center of the sphere and k represents Coulomb’s constant, whose value is $9\times {10}^{9}N.m^2/C^2$.

Substitute the values in the above equation.

$\begin{array}{rcl}E& =& \left(9\times {10}^{9}N.m^2/C^2\right)\left[\frac{5\times {10}^{-9}C}{{\left(4cm\times {\displaystyle \frac{{10}^{-2}m}{1cm}}\right)}^2}\right]\\ & \approx & 2.81\times {10}^{4}N/C\end{array}$

Hence, the magnitude of the electric field due to the sphere at a location 4cm from the center of the sphere is, $2.81\times {10}^{4}N/C$.