Question

a charge of 4×10^-9 C is distributed uniformly over the circumference of a conducting ring of radius 0,3 m calculate the electric field at a point on the axis of ring at 0.4 m from its Centre and also from centre.

Answer 1

Dear Student,

Given,

Radius of the ring, $r=0.3\mathrm{m}$
Change on the ring, $q=4\times {10}^{-9}\mathrm{C}$
Expression for the electric field at a point on the axis of the ring at distance x from the centre of the ring is given as
$$\begin{gathered} E_x=\frac{qx}{4\pi {\epsilon }_0{\left(x^2+r^2\right)}^{3/2}} \\ \Rightarrow E_x=\frac{9\times {10}^9\times 4\times {10}^{-9}\times 0.4}{{\left(0.4^2+0.3^2\right)}^{3/2}} \\ \Rightarrow E_x=115.2\mathrm{N}/\mathrm{C} \end{gathered}$$

Electric field at the centre of the ring is
$$\begin{gathered} E_x=\frac{qx}{4\pi {\epsilon }_0{\left(x^2+r^2\right)}^{3/2}} \\ \mathrm{When},r=0 \\ \Rightarrow E_{x=0}=0 \end{gathered}$$

Regards,