Concept:
The discovery of the magnetic effect of electric current established the relationship between electricity and magnetism and became the foundation of electromagnetism.
Step 1: Understand the historical experiment.
In the year 1820, Danish scientist Hans Christian Oersted performed an experiment in which he placed a compass needle near a current-carrying conductor.
Step 2: Observe the result.
When electric current passed through the wire, the compass needle got deflected from its normal north-south direction.
This proved that electric current produces a magnetic field around the conductor.
Step 3: Identify the scientist.
Therefore, the magnetic effect due to electric current was discovered by:
\[
\boxed{\text{Oersted}}
\]
Hence, the correct option is (3).