Elements that easily transmit electricity and heat display the property known as conductivity.
a. true
b. false

True.

Conductivity is the ability to transmit heat, electricity or sound. Conductivity is a physical property.

A physical property is one which can be measured  or observed without changing the composition or identity of a the substance.

Conductivity is a physical property because the composition of the substance does not change.

A copper wire is still  a copper wire when it is conducting electricity. Like wise, an aluminum rod is still an aluminum rod when heated. It is conducting heat but the heat does not change it, it is still  an aluminum rod during the whole process.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.