A cube of side b has a charge q at each of it | vedclass

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

Question

(C) The length of the side of the cube is $b$.There is a charge $q$ at each of its $8$ vertices.The distance from the centre of the cube to any vertex

Vedclass · Accepted Answer

$\frac{4 q}{\sqrt{3} \pi \epsilon_{0} b}$

Vedclass · Answer

(C) The length of the side of the cube is $b$.There is a charge $q$ at each of its $8$ vertices.The distance from the centre of the cube to any vertex is $r = \frac{1}{2} 	imes 	ext{diagonal of the cube}$.The diagonal of the cube is $\sqrt{b^2 + b^2 + b^2} = b\sqrt{3}$.Thus,$r = \frac{b\sqrt{3}}{2}$.The electric potential $V$ at the centre due to one charge is $V_1 = \frac{1}{4\pi\epsilon_0} \frac{q}{r}$.Since there are $8$ charges,the total potential $V = 8 	imes V_1 = 8 	imes \frac{1}{4\pi\epsilon_0} \frac{q}{(b\sqrt{3}/2)}$.$V = \frac{8q}{4\pi\epsilon_0} 	imes \frac{2}{b\sqrt{3}} = \frac{4q}{\sqrt{3}\pi\epsilon_0 b}$.The electric field at the centre due to each charge is directed away from the charge (if $q>0$) towards the opposite vertex. Since the charges are placed symmetrically,the electric field vectors from opposite vertices cancel each other out. Therefore,the net electric field at the centre is $0$.

$A$ cube of side $b$ has a charge $q$ at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube.

Similar Questions

The dimensions of electric potential are

Assertion : Two concentric charged shells are given. The potential difference between the shells depends on the charge of the inner shell.
Reason : Potential due to the charge of the outer shell remains the same at every point inside the sphere.

$A$ particle '$A$' has charge '$+q$' and a particle '$B$' has charge '$+4q$'. Each has the same mass '$m$'. When they are allowed to fall from rest through the same potential difference '$V$',the ratio of their speeds will be (particle $A$ to particle $B$):

If an electron moves from rest from a point at which potential is $50\, V$ to another point at which potential is $70\, V$,then its kinetic energy in the final state will be:

The electric potential at the center $O$ of two concentric half rings of radii $R_1$ and $R_2$, having the same linear charge density $\lambda$, is $(\epsilon_0 = \text{permittivity of free space})$:

Vedclass Test Series

Exam Paper Generator

Online Exam Module