Particle A with charge $Q$ and particle B with charge $2 Q$ are fixed at positions $\vec{r}_A$ and $\vec{r}_B$, respectively. The force on $A$ due to $B$ is $\vec{F}_{B A}$, and that on $B$ due to $A$ is $\vec{F}_{A B}$. Which of the following options is correct?

The magnetic fux $\phi_B(t)$ through a coil at a time $t$ is given by $\phi_B(t)=\phi_0 \cos \omega t$, where $0 \leq$ $\omega t \leq \pi$ and $\phi_0$ is a non-zero constant. At what time is the magnitude of the induced emf a maximum?

The intrinsic electron and hole concentrations of a Si-based intrinsic semiconductor are $n_e^{(0)}$ and $n_h^{(0)}$, respectively. Upon doping with trivalent impurities the respective carrier concentrations become $n_e$ and $n_h$. Which of the following options is true?

The velocity $v(t)$ of a particle moving in one dimension is given by:

$$ v(t)= \begin{cases}\alpha t, & 0 \leq t \leq T / 3 \\ \alpha T / 3, & T / 3 \leq t \leq 2 T / 3 \\ \alpha(T-t), & 2 T / 3 \leq t \leq T\end{cases} $$

where $\alpha(\neq 0)$ is a constant. What is the displacement of the particle from time $t=0$ to $T$ ?