A thin square plate is placed in the x-y plan | vedclass

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

Question

(D) The total charge $Q$ on the plate is given by the surface integral of the charge density $\sigma$ over the area of the plate:$Q = \int_{-a}^{a} \i

Vedclass · Accepted Answer

Zero

Vedclass · Answer

(D) The total charge $Q$ on the plate is given by the surface integral of the charge density $\sigma$ over the area of the plate:$Q = \int_{-a}^{a} \int_{-a}^{a} \sigma_0 xy \, dx \, dy$$Q = \sigma_0 \left( \int_{-a}^{a} x \, dx ight) \left( \int_{-a}^{a} y \, dy ight)$Since the integral of an odd function over a symmetric interval $[-a, a]$ is zero:$\int_{-a}^{a} x \, dx = 0$ and $\int_{-a}^{a} y \, dy = 0$Therefore,$Q = \sigma_0 	imes 0 	imes 0 = 0$.Alternatively,by symmetry,the charge in the first quadrant is positive,the second is negative,the third is positive,and the fourth is negative. Due to the symmetry of the function $\sigma = \sigma_0 xy$ about the axes,the total charge sums to zero.

$A$ thin square plate is placed in the $x-y$ plane as shown in the figure,such that its center coincides with the origin. Its charge density at point $(x, y)$ is $\sigma = \sigma_0 xy$ (where $\sigma_0$ is a constant). Find the total charge on the plate.

Similar Questions

Each of two large conducting parallel plates has one-sided surface area $A$. If one of the plates is given a charge $Q$ whereas the other is neutral,then the electric field at a point in between the plates is given by

Give definitions of linear,surface,and volume charge densities and write their $SI$ units.

$A$ non-uniformly shaped conductor is charged. Then,at its sharpest point:

If on two concentric hollow spheres of radii $r$ and $R$ $(R > r)$,the total charge $Q$ is distributed such that their surface charge densities are equal,then the potential at their common centre is:

The radius of a charged metal sphere $(R)$ is $10 \, cm$ and its potential is $300 \, V$. Find the charge density on the surface of the sphere.

Vedclass Test Series

Exam Paper Generator

Online Exam Module