During a thunderstorm, a small positively charged object $($e$.$g$.,$ a charged droplet or dust

particle$)$ is located near a grounded metallic sphere $($acting as a lightning rod cap$).$ The

sphere, of radius R $=0\mathrm{.}05$ m$,$ is grounded, ensuring it remains at zero potential. The

charged particle has a charge of q $=+2\mathrm{.}0$ C and is initially located at a distance d $=$

$0\mathrm{.}10$ m from the sphere's center.

a$.$ Calculate the force acting on the charged object due to its interaction with the

grounded sphere.

b$.$ Determine the work required to bring the charged particle closer, from d $=0\mathrm{.}10$ m to

d $=0\mathrm{.}06$ m$.$

c$.$ Discuss how this principle applies to designing lightning rods or other grounded objects

used to mitigate electric field concentration during thunderstorms.