A conducting sphere is charged so that it has a uniform surface charge density of $=+1\mathrm{.}45\frac{C}{m}?$ At a point $P,$ located $r=2\mathrm{.}50m$ from the centre of the sphero, you measure the electric polential to be $V_1=420V,$ see Figure $1.$ Assume the potential is zero very far from the sphere.

A$)$ What is the charge $Q$ and radius $R$ of the sphere? What is the electric field very close to its surface?

B$)$ A tiny metal droplet with mass $m=0\mathrm{.}0200g$ and charge

Problem $1$

A conducting sphere is charged so that it has a uniform surface charge density of $=+1\mathrm{.}45Cm?$ At a point $P_1$ located $r=2\mathrm{.}50m$ from the centre of the sphere, you measure the electric potential to be $V_i=420V,$ see Figure $1.$ Assume the potontial is zero very far from the sphere.

A$)$ What is the charge $Q$ and radius $R$ of the sphere? What is the electric fieid very close to its surface?

B$)$ A tiny metal droplet with mass $m=0\mathrm{.}0200g$ and charge $)=(-3\mathrm{.}00{10}^{-10}C$ is placed at rest at $P,$ and begins to accelerate towards the larger sphere. What is the speed of the droplet when it reaches the point $P_2$ halfway between $P_1$ and the centre of the large sphere? is outside the sphere.$)$

C$)$ The large sphere is now charged to $Q=0\mathrm{.}24C$ and then connected through a thin conducting wire to a second, initially uncharged sphere with radius $\frac{R}{2},$ i$.$e$.$ with half the radius of the larger sphere. What will be the final charges $Q_1$ and $Q_2$ on each sphere? $($You can assume that the charge on the connecting wire is negligilie$)$