Question

FIGURE P25.66 shows two uniformly charged spheres.

What is the potential difference between points$a\mathrm{and}b$?

Which point is at the higher potential?

Short answer

The potential at point 'b' is larger.

Step-by-step solution

Given information and theory used

Given figure :

Theory used :

The potential for each point will be determined as $V=\underset{i}{k\sum }\frac{q_i}{r_i}$,

where$r$ is the distance between the point in question and the charge $q$.

Determining the potential difference between points a and bwhich point is at the higher potential

It's important to remember that the electric potential is a scalar number, which means we may add the potentials from the two charges for each of the two places. We must also regard the spheres as point charges positioned in the center of the sphere.

The spheres' radii will undoubtedly be $30cm\mathrm{and}5cm$, respectively.

Having said that, we have

$V_a=9\times {10}^9(\frac{1\times {10}^{-7}}{0.3}+\frac{2.5\times {101}^{-8}}{0.7})=\mathbf{}\mathbf{3}\mathbf{.}\mathbf{3}\mathbf{}\mathit{k}\mathit{V}$

for point 'a'.

Point b, on the other hand, will have

$V_b=9\times {10}^9(\frac{1\times {10}^{-7}}{0.95}+\frac{2.5\times {101}^{-8}}{0.05})=\mathbf{}\mathbf{5}\mathbf{.}\mathbf{4}\mathbf{}\mathit{k}\mathit{V}$

As a result of this, it is clear that the potential at point b is larger.