Two sides of the same sphere

Electricity and Magnetism Level 5

There exists a uniformly charged, thin solid hemispherical shell of radius $R$ and constant thickness $t$ with surface charge density $\sigma$ . If the force experienced by one hemisphere of this shell due to the electrostatic field of the other can be expressed as:

$\frac { \pi k }{ { \varepsilon }_{ 0 } } \times { 10 }^{ p }$

Find the remainder when $k+p$ is divided by $10$ .

Details and Assumptions:

${ \varepsilon }_{ 0 }$ is the permittivity of free space.
Assume $t<<R$ .
$t=2 mm$
$R=6 m$
$\sigma = 7 Cm^{-2}$
$k$ is a natural number while $p$ is an integer. $k$ is not divisible by $10$ .

9 3 0 4 5 8 1 2

1 solution

Nishant Rai
Apr 17, 2015

$Force = \frac { \sigma^2 \pi R^2}{2 {\varepsilon}_{0}}$

$\rightarrow Pressure = \frac { \sigma^2 }{2 {\varepsilon}_{0}}$

$\Rightarrow Pressure = \frac{F}{\pi R^2}$

The pressure at the surface is contributed by the electric field due to all other charges.But here we are considering the field due to only one hemisphere.so isn't it incorrect.

Spandan Senapati - 4 years ago

But the forces between elements of same hemisphere cancel out.

Rayyan Shahid - 3 years, 2 months ago

Two sides of the same sphere

1 solution

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