Consider a metal sphere of radius R that is c | vedclass

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

Question

(D) The electrostatic pressure on the surface of a charged conductor is given by $P = \frac{\sigma^2}{2\epsilon_0}$,where $\sigma$ is the surface char

Vedclass · Accepted Answer

$\frac{Q^2(R^2 - h^2)}{32\pi \epsilon_0 R^4}$

Vedclass · Answer

(D) The electrostatic pressure on the surface of a charged conductor is given by $P = \frac{\sigma^2}{2\epsilon_0}$,where $\sigma$ is the surface charge density.Given the total charge $Q$ on a sphere of radius $R$,the surface charge density is $\sigma = \frac{Q}{4\pi R^2}$.Thus,the pressure is $P = \frac{1}{2\epsilon_0} \left( \frac{Q}{4\pi R^2} ight)^2 = \frac{Q^2}{32\pi^2 \epsilon_0 R^4}$.The force required to hold the two parts together is equal to the force exerted by this pressure over the cross-sectional area of the cut.The cross-sectional area of the plane cut at distance $h$ from the center is $A = \pi r^2$,where $r^2 = R^2 - h^2$. So,$A = \pi(R^2 - h^2)$.The total force $F$ is $F = P 	imes A = \left( \frac{Q^2}{32\pi^2 \epsilon_0 R^4} ight) 	imes \pi(R^2 - h^2) = \frac{Q^2(R^2 - h^2)}{32\pi \epsilon_0 R^4}$.

Consider a metal sphere of radius $R$ that is cut in two parts along a plane whose minimum distance from the sphere's centre is $h$. The sphere is uniformly charged by a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together is:

Similar Questions

$A$ slit of width $a$ is illuminated by red light of wavelength $6500 \,\, \mathring{A}$. The first minimum will fall at $\theta = 30^{\circ}$ if $a$ is equal to:

Given that,$a \alpha^2+2 b \alpha+c \neq 0$ and that the system of equations
$\begin{aligned} & (a \alpha+b) x+a y+b z=0 \\ & (b \alpha+c) x+b y+c z=0 \\ & (a \alpha+b) y+(b \alpha+c) z=0\end{aligned}$
has a non-trivial solution,then $a, b$ and $c$ lie in

In Whittaker's classification system,which kingdom acts as the primary producer?

The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal:
$Fe_2O_{3(s)} + 3CO_{(g)} \rightleftharpoons 2Fe_{(l)} + 3CO_{2(g)}$
Using the Le Chatelier's principle,predict which one of the following will not disturb the equilibrium?

Define the octet rule. Write its significance and limitations.

Vedclass Test Series

Exam Paper Generator

Online Exam Module