Since the velocity \(vec{v}\) is parallel to the magnetic field \(vec{B}\), the magnetic force is zero. The electric field exerts a force opposite to the direction of velocity on the negatively charged electron, decreasing its speed.

The speed of light in free space is \(c = \frac{1}{\sqrt{\varepsilon_0\mu_0}}\) and in a medium is \(v = \frac{1}{\sqrt{\varepsilon\mu}}\). The refractive index \(n = \frac{c}{v} = \sqrt{\frac{\varepsilon\mu}{\varepsilon_0\mu_0}} = \sqrt{2 \times 1.5} = \sqrt{3}\).

For the wire to be suspended, the upward magnetic force must equal gravity: \(I L B = mg ⇒ I = \frac{mg}{LB}\). Plugging in the values: \(I = \frac{0.250 \times 9.8}{2 \times 0.7} = 1.75\text{ A}\).

Inside the hollow pipe, the magnetic field is zero according to Ampere's law. Since a current-carrying pipe is electrically neutral, the electric field outside the pipe is zero.

Frequency of revolution in a magnetic field is given by \(f = \frac{qB}{2\pi m}\). Since the electron has the highest charge-to-mass ratio \(q/m\) among the charged particles, it has the maximum frequency.

For circle: \(M = I \pi R^2\) where \(2\pi R = L ⇒ R = \frac{L}{2\pi}\), so \(M = \frac{I L^2}{4\pi}\). For square of side \(a = \frac{L}{4}\): \(M' = I a^2 = \frac{I L^2}{16}\). Thus, \(M' = \frac{\pi}{4} M\).

The magnetic force \(\vec{F} = Q(\vec{v} \times \vec{B})\) is always perpendicular to the velocity \(\vec{v}\). Therefore, power \(P = \vec{F} \cdot \vec{v} = 0\), meaning the work done is always zero.

The magnetic force is given by \(F = qvB\sin\theta\). If the particle moves across the field lines, \(\sin\theta \neq 0\), resulting in a non-zero force.

Diamagnetic substances have negative magnetic susceptibility because they develop magnetization in a direction opposite to the applied magnetic field.

Current sensitivity is given by \(I_s = \frac{NBA}{C}\). To increase it, we need to increase \(N\), \(B\), \(A\) or decrease \(C\). None of the options perform these changes.