Question

Question: A \({\bf{ + 3}}{\bf{.5}}\;{\bf{\mu C}}\) charge is 23 cm to the right of a \({\bf{ - 7}}{\bf{.2}}\;{\bf{\mu C}}\) charge. At the midpoint between the two charges, (a) determine the potential and (b) the electric field.

Short answer

(a) The potential at the midpoint between the two charges is \( - 2.9 \times {10^5}\;{\rm{V}}\).

(b) The electric field at the midpoint between the two charges is \(7.28 \times {10^6}\;{{\rm{V}} / {\rm{m}}}\).

Step-by-step solution

Understanding of electric potential

The electric potential value can be obtained by dividing the value of the electric potential energy by the magnitude of the charge. Its value is directly related to the value of the electric potential energy.

Given information

The positive charge is, \({Q_1} = 3.5\;{\rm{\mu C}}\)

The negative charge is, \({Q_2} = - 7.2\;{\rm{\mu C}}\)

The separation between the charges is, \(d = 23\;{\rm{cm}}\)

Evaluation of the midpoint between the two charges

The midpoint between the two charges can be calculated as:

\(\begin{aligned}{c}r &= \frac{d}{2}\\ &= \frac{{\left( {23\;{\rm{cm}}} \right)\left( {\frac{{{\rm{1}}{{\rm{0}}^{{\rm{ - 2}}}}\;{\rm{m}}}}{{{\rm{1}}\;{\rm{cm}}}}} \right)}}{2}\\ &= 0.115\;{\rm{m}}\end{aligned}\)

(a) Evaluation of the potential at the midpoint between the two charges

The potential at the midpoint between the two charges can be calculated as:

Thus, the potential at the midpoint between the two charges is \( - 2.9 \times {10^5}\;{\rm{V}}\).

(b) Evaluation of the electric field at the midpoint between the two charges

The electric field at the midpoint between the two charges can be calculated as:

Thus, the electric field at the midpoint between the two charges is \(7.28 \times {10^6}\;{{\rm{V}} / {\rm{m}}}\).