A metal sphere of radius 1 m is charged with | vedclass

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

Question

(C) The electrostatic pressure (stress) on the surface of a charged conductor is given by $P = \frac{\sigma^{2}}{2 \epsilon_{0}}$.Here,the surface cha

Vedclass · Accepted Answer

$\frac{10^{-15}}{8 \epsilon_{0}}$

Vedclass · Answer

(C) The electrostatic pressure (stress) on the surface of a charged conductor is given by $P = \frac{\sigma^{2}}{2 \epsilon_{0}}$.Here,the surface charge density $\sigma = \frac{q}{4 \pi r^{2}} = \frac{10^{-2}}{4 \pi (1)^{2}} = \frac{10^{-2}}{4 \pi} \ C/m^{2}$.Substituting $\sigma$ into the pressure formula: $P = \frac{1}{2 \epsilon_{0}} \left( \frac{10^{-2}}{4 \pi} ight)^{2} = \frac{10^{-4}}{32 \pi^{2} \epsilon_{0}}$.Volume strain is defined as $	ext{strain} = \frac{	ext{stress}}{B}$,where $B$ is the bulk modulus.Given $B = \frac{10^{11}}{4 \pi^{2}}$.Therefore,$	ext{strain} = \frac{10^{-4}}{32 \pi^{2} \epsilon_{0}} 	imes \frac{4 \pi^{2}}{10^{11}} = \frac{10^{-4}}{8 \epsilon_{0} 	imes 10^{11}} = \frac{10^{-15}}{8 \epsilon_{0}}$.

$A$ metal sphere of radius $1 \ m$ is charged with $10^{-2} \ C$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \ N/m^2$. The volume strain in the sphere is $(\epsilon_{0} = \text{permittivity of free space})$

Similar Questions

For the given circuit,calculate the charge on each capacitor in steady state in $\mu C$.

Two capacitors,one of capacitance $C$ and the other of capacitance $C/2$,are connected in parallel to a battery of potential difference $V$. Calculate the heat produced in the connecting wires.

Assuming the drops to be spherical,$27$ identical drops of mercury are charged simultaneously to the same potential of $20 \ V$. If all the charged drops are made to combine to form one big drop,then the potential of the big drop will be: (in $V$)

Find $V_A - V_B$ for the following given circuit in volts.

As shown in the figure,what will be the charge on each capacitor and the potential difference across each,respectively?

Vedclass Test Series

Exam Paper Generator

Online Exam Module