Question

The energy stored in the magnetic field produced by a metal sphere is $4.5J$. If the sphere contains $4\mu C$charge, its radius will be:
[Take: $1/4\pi { \in _o} = 9 \times {10^9}N - {m^2}/{C^2}$]
A. $32mm$
B. $16mm$
C. $20mm$
D. $28mm$

Answer 1

Hint First it is important to check the kind of sphere, hollow or solid. Then the formulas and the EFL or MFL are induced and are calculated step by step.

Complete step-by-step solution :Capacity of an Isolated Spherical Conductor -
$C = 4\pi { \in _o}R = R/9 \times {10^9}$
Therefore the energy stored in the electricity field produced by a metal sphere = 4.5 J
By the comparison we get
$\Rightarrow 4.5 = {Q^2}/2C \\\ \Rightarrow C = {Q^2}/2 \times 4.5 \\\$
Now the capacitance of a spherical capacitor
$C = 4\pi { \in _o}R = {Q^2}/9 \\\ \Rightarrow R = 9 \times {10^9} \times (16/9) \times {10^{12}} \\\ \Rightarrow R = 16 \times {10^{ - 3}} \\\ \Rightarrow R = 16mm \\\$

Note: The distribution of charge is important in these cases. The type of Spheer and subsequent formulas for the types plays a vital role are commonly repeated mistakes over and over again. The shape also is important for the geometrical orientation