KCET2014PhysicsCurrent Electricity
A spherical conductor of radius ( 2 ~cm ) is uniformly charged with ( 3 nC ). What is the electric field at a distance of ( 3 ~cm ) from the center of the sphere?
Options
- A( 3 10⁶ Vm ⁻¹ )
- B( 3 Vm ⁻¹ )
- C( 3 10⁴ Vm ⁻¹ )
- D( 3 10⁻⁴ Vm ⁻¹ )
Correct answer
C. ( 3 10⁴ Vm ⁻¹ )
Step-by-step solution
Electric field at a point at distance ' ( r ) ' is given as ( E= 1 4 ₀ q r² ) Here, ( q=3 nC =3 10⁻⁹ C ; r=3 ~cm =3 10⁻² ~m ) Therefore, ( E= (9 10^ ) 3 10⁻⁹ (3 10⁻² )² = 9 10⁹ 3 10⁻⁹ 9 10⁻⁴ ) ( =3 10⁴ ~V ~m ⁻¹ ) Thus, electric field at a distance of ( 3 ~cm ) from center of the sphere carrying charge ( 3 nC ) is ( 3 10⁴ Vm ⁻¹ )