Question

Two rings of radius 2 cm are 20 cm apart and concentric with a common horizontal x axis. What is the magnitude of the electric field midway between the rings if both rings carry a charge of +35 nC?

Short answer

The magnitude of the net electric field in midway of the rings is $0$.

Step-by-step solution

Identification of given data

The given data can be listed below,

• The radius of two rings is, $r_1=2\mathrm{cm}$.
• The distance between rings is, $d=20cm$.
• The charge on both rings is,$q=+35nC=35\times {10}^{-9}C$

Concept/Significance of electric field

The vector representation of an electric field the amplitude and direction of the electric field are also considered when determining the intensity of the electric field.

Determination of the magnitude of the electric field midway between the rings if both rings carry a charge of +35 nC

The observation point lies in the midway between the two identical rings concentric with a common axis, and both carry charges with the same magnitude and sign. Assume that the common axis of both rings at the centre along the -axis, and since the second ring has a positive component as the final position is greater in magnitude than the initial position. In contrast, the first ring has a negative component as the final position is smaller in magnitude than the initial position. The second ring has an electric field with a positive direction toward the first, and the first ring has an electric field with a negative direction toward the second. i.e., since both rings have the same radius, charge values and are located at equal distance from the observation point, thus both rings exert an electric field with the same magnitude but in opposite rings,

i.e.,

$E_1=E_2$

The net electric field is given by,

$\begin{array}{c}{E}_{net}=E_1+E_2\\ =E_1-E_1\\ =E_2-E_2\\ =0\end{array}$

Thus, the magnitude of the net electric field in midway of the rings is $0$.