Question

What is the electric potential at the point indicated a dot in FIGURE EX25.31?

Short answer

The value of electric potential of the dot point of the figure25.31 is$1.7\times {10}^{2}m$

Step-by-step solution

Theory electric potential 

The electric potential equation of a dot points

$V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$

where the q is the charge points, r is the distance and ${\epsilon }_0$permittivity free space

For the multiple Points $\sum _i{V}_i=\frac{1}{4\pi {\epsilon }_0}\frac{q_i}{r_i}$

From the given triangle, all distances from O to other points A, B, C are equal.

Due to these facts,$OA=OB=OC$

$OA=OB=OC$

Value Calculation 

Now, the length of the bc is equal to

$\begin{array}{rcl}\frac{1}{2}AC& =& \frac{1}{2}(3.0)cm\\ & =& 1.5cm\end{array}$

On the basis of the right-angle triangle

the length of

$\begin{array}{rcl}OC& =& \frac{bC}{\cos \angle ObC}\\ & =& \frac{1.5cm}{\cos \angle 30°}\\ & =& 1.7\times {10}^{-2}\\ & & \end{array}$

The Value of the Electric Potential of the dot point is

$1.7\times {10}^{-2}$

Theory electric potential 

The electric potential equation of a dot points

$V=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r}$

where the q is the charge points, r is the distance and${\epsilon }_0$ permittivity free space

For the multiple Points$\sum _i{V}_i=\frac{1}{4\pi {\epsilon }_0}\frac{q_i}{r_i}$

From the given triangle, all distances from O to other points A, B, C are equal.

Due to these facts,$OA=OB=OC$