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

If a solid and a hollow conducting sphere have the same radius, then:

The figure shows a charged conductor resting on an insulating stand. If at point $P$ the charge density is $\sigma$,the potential is $V$,and the electric field strength is $E$,what are the values of these quantities at point $Q$?

$A$ uniformly charged conducting sphere of $2.4 \, m$ diameter has a surface charge density of $80.0 \, \mu C m^{-2}$. The charge on the sphere is nearly

$A$ point charge $q$ is situated at a distance $r$ on the axis from one end of a thin conducting rod of length $L$ having a charge $Q$ (uniformly distributed along its length). The magnitude of the electric force between the two is . . . . . . .

What are linear,surface and volume distribution of charge?

Vedclass Test Series

Exam Paper Generator

Online Exam Module