Current density is a:
(A) vector expressed in $A{m^{ - 1}}$
(B) scalar expressed in $A{m^{ - 2}}$
(C) vector expressed in $A{m^{ - 2}}$
(D) scalar expressed in $A{m^{ - 1}}$

Hint: In general, there are two types of quantities, one is scalar quantities and the other is vector quantity. The scalar quantities will have only the magnitude and the vector quantity will have both magnitude and direction. According to this statement, the current density is which type of quantity is determined.

Complete answer:
Current density is critical to the plan of electrical and electronic frameworks. Circuit execution relies unequivocally on the planned current level, and the current density at that point is dictated by the components of the leading components. For instance, as incorporated circuits are diminished in size, in spite of the lower current requested by more modest gadgets, there is a pattern toward higher current densities to accomplish higher gadget numbers in ever more modest chip regions. See Moore's law.
At high frequencies, the leading area in a wire gets bound close to its surface which builds the current density in this locale. This is known as the skin impact. High current densities have bothersome results. Most electrical channels have a limited, positive obstruction, causing them to disperse power as warmth. The current density must be kept adequately low to keep the conveyor from dissolving or catching fire, the protecting material fizzling, or the ideal electrical properties evolving. The investigation and perception of current density additionally is utilized to test the material science hidden the idea of solids, including metals, yet in addition semiconductors and encasings. An expanded hypothetical formalism has been created to clarify numerous principal perceptions. The current density is the amount of the current flow per unit area of the cross section.
Current density is given by the formula, $J= \dfrac{I}{A}$
where,I is the current flowing through the conductor
  A is the area of the cross section.

Hence, the option (C) is the correct answer.

Note:
At high current densities the material shaping the interconnections really moves, a wonder called electromigration. In superconductors exorbitant current density may produce a sufficiently attractive field to cause unconstrained loss of the superconductive property.