Question

If a metal cube of side 5

c.m has a charge density of 6 microcoulomb then what is the surface charge density

Answer 1

The surface charge density of the metal cube is 4 × 10⁻⁴ C/m⁻².

Given:

Side of cube (a) = 5 cm = 0.05 m

Charge density (q) = 6μC = 6 × 10⁻⁶ C

To Find:

Surface charge density =?

Solution:

Area of cube = 6a² = 6 × (0.05)²

Charge density (q) = 6 × 10⁻⁶ C

Surface charge density = $\frac{q}{area}$

$= \frac{6 (10^{-6} )}{6 (0.05^{2} )}$

= 400 × 10⁻⁶

= 4 × 10⁻⁴ C/m⁻²

Hence, the surface charge density of the cube is 4 × 10⁻⁴ C/m⁻²

Answer 2

The surface charge density of the metal cube is 4 × 10⁻⁴ C/m⁻².

Given,

Side of cube = 5 cm = 0.05 m

Charge density = 6μC = 6 × 10⁻⁶ C

To Find,

The surface charge density.

Solution,

The formula for calculating the surface charge density is

Surface charge density = q/area

Now,

The area of cube = 6a² = 6 × (0.05)²

Charge density (q) = 6 × 10⁻⁶ C

Now, substituting the values in the formula

Surface charge density = 6 × 10⁻⁶/6 × (0.05)²

Surface charge density = 4 × 10⁻⁴ C/m⁻²

Hence, the surface charge density of the cube is 4 × 10⁻⁴ C/m⁻²

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