Six point charges are kept 60^{circ} apart fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the magnitude of the electric field due to a single charge $Q$ at the center be $E_{0} = \frac{1}{4\pi\epsilon_{0}} \frac{Q}{R^{2}}$.By analyz

Vedclass · Accepted Answer

$ -\frac{Q}{4\pi\epsilon_{0}R^{2}}(\sqrt{3}\hat{i}-\hat{j}) $

Vedclass · Answer

(B) Let the magnitude of the electric field due to a single charge $Q$ at the center be $E_{0} = \frac{1}{4\pi\epsilon_{0}} \frac{Q}{R^{2}}$.By analyzing the symmetry, the charges at $90^{\circ}$ and $270^{\circ}$ (both $+Q$) cancel each other out.The remaining charges are at $30^{\circ}, 150^{\circ}, 210^{\circ}, 330^{\circ}$.Specifically, the charges at $30^{\circ}$ and $210^{\circ}$ are $+Q$ and $+Q$, and at $150^{\circ}$ and $330^{\circ}$ are $-Q$ and $+Q$.Using the principle of superposition, the net electric field is the vector sum of individual fields.After resolving the components, the net electric field at the center is calculated as $\vec{E}_{net} = -\frac{Q}{4\pi\epsilon_{0}R^{2}}(\sqrt{3}\hat{i}-\hat{j})$.

Six point charges are kept $60^{\circ}$ apart from each other on the circumference of a circle of radius $R$ as shown in the figure. The net electric field at the centre of the circle is . . . . . . . ($ \epsilon_{0} $ is the permittivity of free space)

Similar Questions

The figure shows a rod $AB$,which is bent in a $120^{\circ}$ circular arc of radius $R$. $A$ charge $(-Q)$ is uniformly distributed over the rod $AB$. What is the electric field $\overrightarrow{E}$ at the centre of curvature $O$?

$A$ spherical conductor of radius $2 \text{ cm}$ is uniformly charged with $3 \text{ nC}$. What is the electric field at a distance of $3 \text{ cm}$ from the center of the sphere?

Three charges $2q, -q$ and $-q$ are located at the vertices of an equilateral triangle. At the center of the triangle,

$A$ metal sphere of radius $R \ cm$ is charged with $4 \pi \mu C$ and is situated in air. If $\sigma$ is the surface charge density and $E$ is the electric intensity at a distance $r$ from the centre of the sphere,then $r$ is equal to ($\epsilon_{0}$ is the permittivity of free space).

An infinite line charge produces a field of $9 \times 10^4 \text{ NC}^{-1}$ at a distance of $2 \text{ cm}$. Calculate the electric field produced at a distance of $3 \text{ cm}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module