Question

A charge of 0.91 C is spread uniformly throughout a 25 cm rod of radius 4 mm. What are the volume and linear charge densities

Answer 1

The volume of the rod is 1.26×10⁻⁵ m³, and the linear charge density of the rod is 3.64 C/m

What is volume?:

This is the product of the height of a solid object and its crossectional area.

The Volume of the rod is can be calculated using the formula below.

Note: A rod has the shape of a cylinder.

Formula:

• V = πr²h............... Equation 1

Where:

• V = Volume of the rod
• r = radius of the rod
• h = height of the rod.

From the question,

Given:

• r = 4mm = 0.004 m
• h = 25 cm = 0.25 m
• π = 3.14

Substitute these values into equation 1

• V = 3.14(0.004²)(0.25)
• V = 1.26×10⁻⁵ m³

What is linear charge density:

This is the ratio of the charge on an object to the length of the object.

The linear charge density of the rod can be calculated using the formula below.

• D = Q/h.................... Equation 2

Where:

• D = Linear charge density of the rod
• Q = Charge on the rod.
• h = height or length of the rod

From the question

Given:

• Q = 0.91 C
• h = 25 cm = 0.25 m

Substitute these values into equation 2

• D = 0.91/0.25
• D = 3.64 C/m

Hence, The volume of the rod is 1.26×10⁻⁵ m³, and the linear charge density of the rod is 3.64 C/m

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