Question

A total charge of 6.3 x 10-8 C is placed on a 2.7 cm radius isolated conducting sphere. The surface charge density is: A. 2.55 x 10-4 C/m3 Explain B. 8.64 x 10-5 C/m2 C. 2.75 x 10-5 C/m2 D. 6.88 x 10-6 C/m2 E. 7.43 x 10-7 C/m

Answer 1

Answer:

$6.88\times 10^{-6}\ C/m^2$

Explanation:

Q = Total charge = $6.3\times 10^{-8}\ C$

$\rho$ = Surface charge density

r = Radius = 2.7 cm

A = Surface area = $4\pi r^2$

Charge is given by

$Q=A\rho\\\Rightarrow Q=4\pi r^2\times \rho\\\Rightarrow \rho=\dfrac{Q}{4\pi r^2}\\\Rightarrow \rho=\dfrac{6.3\times 10^{-8}}{4\pi (2.7\times 10^{-2})^2}\\\Rightarrow \rho=0.00000687706544224\\\Rightarrow \rho=6.88\times 10^{-6}\ C/m^2$

The surface charge density is $6.88\times 10^{-6}\ C/m^2$