Question

A tube of mercury with resistivity 9.84 × 10-7 ?? · m has a 23.0 N/C electric field inside the column of mercury. How much current is flowing, if the diameter of the tube is 1mm?
15)
A) 280 A B) 18 A C) 29 A D) 180 A

Answer 1

Concepts and reason

The concepts used in this problem are the resistance of a material and electric field.

First, write the formula for the resistivity of the mercury by using the expression of resistivity of a material and then, determine the cross-sectional area of the mercury surface by using the expression of the cross-sectional area of the mercury surface.

Later, determine the current flowing through the mercury by using the formula of resistivity.

Fundamentals

Resistivity:

The resistivity of a material is defined as the measure of the resistance in the flow of electricity for a given size of a specific material.

The expression for resistivity of the material can be written as,

Here, is the resistivity of the material, is the cross-sectional area of the tube, is current and is electric field.

Electric field:

The electric field can be described as the electric force per unit charge. The direction of the electric field is taken to be in the direction of the electric force exerted on a positive test charge.

The cross-sectional area of the cylindrical surface:

The cross-sectional area of the mercury surface can be written as,

Here, is the cross-sectional area of the tube, is the diameter of the tube.

The resistivity of the mercury can be expressed as,

…… (1)

Here, is the resistivity of the mercury, is the current flowing through the mercury and is electric field inside the column.

The cross-sectional area of the mercury surface can be expressed as,

Substitute for in above expression.

The resistivity of the mercury is given as,

Substitute for, for and for in equation (1).

Rearrange the above equation for

Ans:

The current flowing through mercury is.