Question

Q8 (b) Two identical circular loops '1' and '2' of radius R each have linear charge density – λ and +​λ C/m respectively. The loops are placed coaxially with their centres $R\sqrt{3}$ distance apart. Find the magnitude and direction of the net electric field at the centre of loop '1'.

Answer 1

Dear Student,

If the loops are placed on z-axis, i.e their centres lie on z-axis, At the centre of loop 1 the electric field due to loop 1 will be zero because of symmetry. But there will be and effective field a z-axis due resultant cosine component of the field due to loop 2.

$$\begin{gathered} ElectricFieldalongz-axisduetoaringisgivenas. \\ {E}_z=\frac{kQz}{{\left(z^2+R^2\right)}^{{\displaystyle \frac{3}{2}}}} \\ also,\lambda =\frac{Q}{2\pi R},z=R\sqrt{3} \\ substituting, \\ {E}_z=\frac{k\times \lambda 2\pi R\times R\sqrt{3}}{4^3{R}^3}\Rightarrow \frac{1}{2{\epsilon }_0}\times \frac{\lambda \sqrt{3}}{64R}\Rightarrow \frac{\lambda \sqrt{3}}{128{\epsilon }_{0}R}alongz-axisawayfromtheloops \end{gathered}$$

Regards.