Consider two waves, which are given by $y_1(x, t)=A \sin (k x-\omega t)$ and $y_2(x, t)=\sqrt{3} A \cos (k x-\omega t)$, where $k$ is the wave number and $\omega$ is the angular frequency. The amplitude of the resultant waveform obtained by the superposition of the two waves is $A_s$ and its phase difference with $y_1$ is $\phi_s$. What are $A_s$ and $\phi_s$ ?

A particle of charge $q=1 e$ and mass $m$ with kinetic energy $K$ enters an electric field set up by two parallel plates of length $l$ as illustrated in the figure. The potential difference between the two plates is 1 V and their separation is $d$. What is the minimum value of $K$ (in eV ) for which the particle will not hit either of the plates? [ $e$ is the charge of the electron.]

What is the potential difference between the points $P$ and $Q$ in the circuit shown below, once the capacitors are fully charged?

A particle of mass $m$ and charge $q$ moving with a velocity $\vec{v}=v_0(\hat{i}+\hat{j}-\hat{k})$ is placed in a uniform magnetic field $\vec{B}=B_0(\hat{i}+\hat{j}+\hat{k})$. It executes a helical trajectory of radius $r$ and pitch $p$. Which of the following options is correct?