Step 1: Picture an electromagnetic wave. An electromagnetic wave has an electric field and a magnetic field. They wiggle at right angles to each other and to the direction the wave travels.
Step 2: Recall the field relation. At every instant the size of the electric field $E$ and the magnetic field $B$ are linked by the speed of light $c$: \[ E = cB. \]
Step 3: Apply it to the peak values. The peak, or largest, values follow the same link. So replacing $E$ and $B$ with their peaks gives \[ E_0 = c\,B_0. \]
Step 4: Check the size sense. Since $c$ is a very large number, the electric field value is much larger than the magnetic field value in usual units, which matches everyday measurements.
Step 5: Rule out the wrong forms. $E_0 = B_0$ misses the factor $c$. $B_0 = cE_0$ has the roles swapped. $E_0 = c^2 B_0$ uses the wrong power of $c$.
Step 6: State the answer. The correct relation between the peak fields is the electric peak equals $c$ times the magnetic peak. \[ \boxed{E_0 = cB_0} \]
