Question

A conducting sphere of radius 10 cm. has an unknown charge. If the electric field 20 cm. from the centre of the sphere is 1.5*10^3 N/C and points radially inward, what is the net charge on the sphere

Answer 1

as the electric field is radially inward so charge on sphere is negative.
electric field outside due to a conducting sphere is given by 
E = K*Q / r^2          (K = 9*10^9)
1.5*10^3 = 9*10^9*(-Q) / .2^2
on solving we get 
Q = -20 / 3 nc 

Answer 2

Answer:

• 6.67 nC

Explanation:

Given

• A conducting sphere of radius 10 cm. has an unknown charge
• If the electric field 20 cm. from the centre of the sphere is 1.5×10³ N/C and points radially inward

Tofind

• what is the net charge on the sphere

Solution

$E = \frac{q}{4\pi \varepsilon_{0} d^2}$

Where

• q = Net charge = 1.5 × 10³ N/C

• d = Distance from the center of sphere = 20 cm = 0.2 m

• $\varepsilon_{0}$ = permittivity of free space

• $\frac{1}{4\pi \varepsilon_{0} }$ = 9 × 10$^9$ Nm²C$^{-2}$

$q = E( 4\pi \varepsilon_{0} )d^2$

$= \frac{1.5\times 10^3 \times (0.2)^2}{9\times 10^9}$

$= 6.76 \times 10^9 C$

$= 6.67 \:nC$

Hence

• Net charge on the sphere is 6.67 nC