Question

If the electric potential along a line due to a charge is given by $V\left(r\right)=\frac{25}{r}+3$, where r is the distance from the charge, what is the electric field at a point r = 5 along this line?

• A. $-1\frac{N}{C}$
• B. $1\frac{N}{C}$
• C. $5\frac{N}{C}$
• D. $-5\frac{N}{C}$

Answer 1

The correct option is A $-1\frac{N}{C}$

We are given an r dependent equation for potential. So we can directly find a relation for potential by differentiating the V equation.

\(V(r) = \frac{25}{r} +3\)
$E\left(r\right)=-\frac{dV}{dr}$
$\therefore Er=-\frac{25}{r^2}$
At r = 5, $E\left(5\right)=-\frac{25}{25}$
$E\left(5\right)=-1\frac{N}{C}$