Question

3. A metal sphere of radius 10cm is charged by 4 uc.
Find the electric field
(i) at a point outside the sphere at a distance of 8 cm from the surface
(ii) at a point at a distance of 6 cm from the centre
(iii) on the surface of sphere.
minha​

Answer 1

answer : option (i) 0.11 × 10^7 N/C (ii) 0 (iii) 3.6 × 10^5 N/C

(i) at a point outside the sphere at a distance of 8cm from the surface.

R = 8cm + r = 8cm + 10cm = 18cm

using Gauss's law,

Φ = Q_in/ε0

⇒E.A = 4μC/ε0

⇒E. 4πR² = 4μC/ε0

⇒E = 4μC/4πR²ε0 = K(4μC)/R² [ as 1/4πε0 = K ]

= 9 × 10^9 × 4 × 10^-6/(18 × 10^-2)²

= 36 × 10³/324 × 10-⁴

= 1/9 × 10^7

= 0.11 × 10^7 N/C

(ii) at a point at a distance of 6 cm from the centre

point is inside the sphere. i.e., charge inside the Gaussian surface is zero. electric field at a point at a distance of 6cm from the centre is zero.

(c) on the surface of sphere

electric field , E = kQ/r

= 9 × 10^9 × 4 × 10^-6/10 × 10-²

= 36 × 10³/10-¹

= 3.6 × 10^5 N/C

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

(i) at a point outside the sphere at a distance of 8cm from the surface.

R = 8cm + r = 8cm + 10cm = 18cm

using Gauss's law,

Φ = Q_in/ε0

⇒E.A = 4μC/ε0

⇒E. 4πR² = 4μC/ε0

⇒E = 4μC/4πR²ε0 = K(4μC)/R² [ as 1/4πε0 = K ]

= 9 × 10^9 × 4 × 10^-6/(18 × 10^-2)²

= 36 × 10³/324 × 10-⁴

= 1/9 × 10^7

= 0.11 × 10^7 N/C

(ii) at a point at a distance of 6 cm from the centre

point is inside the sphere. i.e., charge inside the Gaussian surface is zero. electric field at a point at a distance of 6cm from the centre is zero.

(c) on the surface of sphere

electric field , E = kQ/r

= 9 × 10^9 × 4 × 10^-6/10 × 10-²

= 36 × 10³/10-¹

= 3.6 × 10^5 N/C