The dielectric strength of air is 2.0×106 N/C. The largest charge that a metallic sphere of 3 mm radius can hold is

Question

The dielectric strength of air is 2.0×106 N/C. The largest charge that a metallic sphere of 3 mm radius can hold is (A) 2 nC (B) 3 nC (C) 1.5 nC (D) 6 nC

Tardigrade Admin · Accepted Answer

Dielectric strength is the maximum electric field that a pure material can withstand under ideal conditions without breaking down.
Here

E = \frac{Q}{4 π ϵ _{0} R ^{2}}

< b r / >\Rightarrow Q = E .4 π ϵ_{0} R^{2} = 3 \times 1 0^{6} . (4 π \times 8.85 \times 1 0^{- 12} \times 0.3 0^{2} \times 1 0^{- 4}) = 3 \times 1 0^{- 9} C = 3 n C < b r / >

Q. The dielectric strength of air is $2.0 \times 1 0^{6} N / C$ . The largest charge that a metallic sphere of $3 mm$ radius can hold is

2 $n$ C

3 $n$ C

1.5 $n$ C

6 $n$ C

Q. The dielectric strength of air is 2.0×106N/C. The largest charge that a metallic sphere of 3mm radius can hold is

2 nC

3 nC

1.5 nC

6 nC

Dielectric strength is the maximum electric field that a pure material can withstand under ideal conditions without breaking down. Here E=4πϵ0​R2Q​ <br/>⇒Q=E.4πϵ0​R2=3×106.(4π×8.85×10−12×0.302×10−4)=3×10−9C=3nC<br/>

Q. The dielectric strength of air is $2.0 \times 1 0^{6} N / C$ . The largest charge that a metallic sphere of $3 mm$ radius can hold is

2 $n$ C

3 $n$ C

1.5 $n$ C

6 $n$ C