  We discuss the Luttinger Liquid behaviour of Large Radius Carbon Nanotube
e.g. the Multi Wall ones (MWNT), under the action of a transverse magnetic
field $B$. Our results imply a reduction with $B$ in the value of the $bulk$
critical exponent, $\alpha_{bulk}$, for the tunneling density of states, which
is in agreement with that observed in transport experiments. Then, the problem
of the transport through a Quantum Dot formed by two intramolecular tunneling
barriers along the MWNT, weakly coupled to Tomonaga-Luttinger liquids is
studied, including the action of a strong transverse magnetic field $B$. {We
predict the presence of some peaks in the conductance G versus $B$, related to
the magnetic flux quantization in the ballistic regime (at a very low
temperature, $T$) and also at higher $T$, where the Luttinger behaviour
dominates}. The temperature dependence of the maximum $G_{max}$ of the
conductance peak according to the Sequential Tunneling follows a power law,
$G\propto T^{\gamma_e-1}$ with $\gamma_e$ linearly dependent on the critical
exponent, $\alpha_{end}$, strongly reduced by $B$.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons