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 the integral of the pressure component normal to the cross-sectional plane. This is equivalent to the pressure multiplied by the area of the cross-section.The radius of the circular cross-section formed by the plane is $r = \sqrt{R^2 - h^2}$.The area of this cross-section is $A = \pi r^2 = \pi(R^2 - h^2)$.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 into two parts along a plane whose minimum distance from the sphere's centre is $h$. The sphere is uniformly charged with a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together is:

Similar Questions

Consider two concentric spherical metal shells of radii $r_{1}$ and $r_{2}$ $(r_{2} > r_{1})$. If the outer shell has a charge $q$ and the inner one is grounded,the charge on the inner shell is

Under electrostatic condition of a charged conductor,which among the following statements is true?

$A$ metallic spherical shell has an inner radius $R_1$ and an outer radius $R_2$. $A$ charge $Q$ is placed at the center of the spherical cavity. What will be the surface charge density on $(i)$ the inner surface,and $(ii)$ the outer surface?

"The electric field inside the hollow region of a conductor in a uniform electric field is zero". Explain.

Vedclass Test Series

Exam Paper Generator

Online Exam Module