Question 699: Electrostatics & Capacitance

Question

A metal cube of side $$5 \mathrm{~cm}$$ is charged with $$6 \mu \mathrm{C}$$. The surface charge density on the cube is

Accepted Answer

To find the surface charge density of a charged metal cube, we need to determine the charge per unit area. The surface charge density, denoted by $$\sigma$$, is given by:
$$\sigma = \frac{Q}{A}$$
where:
$ Q $ is the total charge on the cube
$ A $ is the total surface area of the cube
The cube has a side length of $ 5 \mathrm{~cm} $, so each side of the cube is $ 5 \mathrm{~cm} $. Since 1 cm = 0.01 m, the side length in meters is:
$$5 \mathrm{~cm} = 0.05 \mathrm{~m}$$
The cube has 6 faces, and the area of one face is given by:
$$	ext{Area of one face} = \left( 0.05 \mathrm{~m} ight)^2 = 0.0025 \mathrm{~m}^2$$
Therefore, the total surface area of the cube is:
$$A = 6 	imes 0.0025 \mathrm{~m}^2 = 0.015 \mathrm{~m}^2$$
The total charge, $ Q $, is given as $ 6 \mu \mathrm{C} $. Converting this to Coulombs:
$$6 \mu \mathrm{C} = 6 	imes 10^{-6} \mathrm{~C}$$
Now, plugging the values into the formula for surface charge density:
$$\sigma = \frac{6 	imes 10^{-6} \mathrm{~C}}{0.015 \mathrm{~m}^2} = 4 	imes 10^{-4} \mathrm{~C} \mathrm{m}^{-2}$$
Therefore, the surface charge density on the cube is:
$$\sigma = 0.4 	imes 10^{-3} \mathrm{~C} \mathrm{m}^{-2}$$
So, the correct answer is:
Option D: $$0.4 	imes 10^{-3} \mathrm{C} \mathrm{m}^{-2}$$

Answer

$$0.125 	imes 10^{-3} \mathrm{C} \mathrm{m}^{-2}$$

Answer

$$0.25 	imes 10^{-3} \mathrm{C} \mathrm{m}^{-2}$$

Answer

$$4 	imes 10^{-3} \mathrm{C} \mathrm{m}^{-2}$$

Answer

$$0.4 	imes 10^{-3} \mathrm{C} \mathrm{m}^{-2}$$

Electrostatics & Capacitance

A metal cube of side $5 \mathrm{~cm} is charged with 6 \mu \mathrm{C}$. The surface charge density on the cube is

Choose the correct answer: