A conducting sphere of radius 5 cm has an unknown charge. The electric field at 10 cm from the centre of the sphere is 1.8 × 103 N / C and points radially inward. What is the net charge on the sphere?

Question

A conducting sphere of radius 5 cm has an unknown charge. The electric field at 10 cm from the centre of the sphere is 1.8 × 103 N / C and points radially inward. What is the net charge on the sphere? (A)  1.8 nC  (B)  2 nC  (C)  1 nC  (D)  1.5 nC

Tardigrade Admin · Accepted Answer

For a conducting charged sphere, the electric field outside the sphere (E)=(1/4 π ε0) (Q/r2) 1.8 × 103=9 × 109 × (Q/(0.1)2) Q=(1.8 × 103 × 10-2/9 × 109) =2 × 10-9 C =2 n C

Q. A conducting sphere of radius $5 c m$ has an unknown charge. The electric field at $10 c m$ from the centre of the sphere is $1.8 \times 1 0^{3} N / C$ and points radially inward. What is the net charge on the sphere?

$1.8 n C$

$2 n C$

$1 n C$

$1.5 n C$

For a conducting charged sphere, the electric field outside the sphere
$(E) = \frac{1}{4 π ε _{0}} \frac{Q}{r ^{2}}$
$1.8 \times 1 0^{3} = 9 \times 1 0^{9} \times \frac{Q}{( 0.1 ) ^{2}}$
$Q = \frac{1.8 \times 1 0 ^{3} \times 1 0 ^{- 2}}{9 \times 1 0 ^{9}}$
$= 2 \times 1 0^{- 9} C$
$= 2 n C$

Q. A conducting sphere of radius 5cm has an unknown charge. The electric field at 10cm from the centre of the sphere is 1.8×103N/C and points radially inward. What is the net charge on the sphere?

1.8nC

2nC

1nC

1.5nC