= Solution
Write $f=(v+h)/\sqrt2$. The <Pauli matrices> give the <weak isospin> operators
$$
\tau^+=\begin{pmatrix}0&1\\0&0\end{pmatrix},\qquad
\tau^-=\begin{pmatrix}0&0\\1&0\end{pmatrix},\qquad
\tau_3=\frac12\begin{pmatrix}1&0\\0&-1\end{pmatrix}.
$$
For the <Higgs doublet> $\Phi=(0,f)^T$ with <weak hypercharge> $Y=1$,
$$
\boxed{\tau^+\Phi=\begin{pmatrix}f\\0\end{pmatrix},\quad
\tau^-\Phi=0,\quad
\tau_3\Phi=\begin{pmatrix}0\\-f/2\end{pmatrix},\quad
Q\Phi=(\tau_3+\tfrac12 I)\Phi=0.}
$$
The <Higgs field> direction, including its <vacuum expectation value>, is electrically neutral. Consequently the electromagnetic <U(1)> leaves the vacuum invariant: <electroweak symmetry breaking> preserves electromagnetism and the <photon> remains massless. The result concerns this neutral vacuum direction; it does not say that both components of the full <Higgs doublet> have zero <electric charge>.
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