Question

A particular metal plate of radius 10 cm is given a charge of 20 uc on its surface. the charge density of the plate is

Answer 1

Given:

A particular metal plate of radius 10 cm is given a charge of 20 uc on its surface.

To find:

The charge density of the plate is ?

Solution:

From given data, we have,

A particular metal plate of radius 10 cm

⇒ r = 10 cm

That plate is given a charge of 20 uc on its surface

⇒ q = 20 uc

Since, the charge is given on its surface, we need to find the surface charge density.

Surface charge density = σ = qA

= 20 uc × πr²

= 20 uc × π × 10²

= 20 × 10-⁶ × 3.14 × 10²

= 20 × 3.14 × 10-⁴  

= 62.8  × 10-⁴ C/cm²

Answer 2

Question:

A circular metal plate of radius 10 cm is given a

charge of 20 μ C on its surface. The charge density of

the plate is

Answer:   6.36 x 10^-4 C/ m²

Explanation:

Since it is a circular metal plate, A = πR² where R = 10 x $10^{-2}$ m

Charge, Q = 20 x $10^{-6}$ C            (1 μ = 10^-6)

Surface Charge Density, σ  = $\frac{Q}{A}$   = $\frac{20 (10^{-6}) }{3.14 (20 (10^{-2}))^{2} } = \frac{20 (10^{-6})}{3.14 (20^{2})(10^{-4}) } = \frac{10^{-2} }{3.14(20)} = 6.36 ( 10^{-4} ) C/m^{2}$

THANKS!