By convention, anode is placed on left and cathode is placed on the right. Oxidation occurs at anode and reduction occurs at the cathode.

Redox reaction for the cell is

Zn(s) + Cu²⁺→Zn²⁺(aq) + Cu(s)

Anode- oxidation half-cell: Zn(s) → Zn²⁺ (aq)+ 2e^-

Cathode- reduction half-cell: Cu²⁺ (aq)+ 2e^-→ Cu(s)

Zinc goes into solution as Zn²⁺ and leaves behind the electrons on Electrode A making it negatively charged. Cu²⁺ from the solution deposits on Electrode B making it positively charged.

Electrode A polarity- negative

Electrode B polarity- positive