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?

A charged particle is moving in a circular orbit with radius $r$ and orbital angular frequency $\omega$ in the presence of a magnetic field. The orbit is enclosed within a larger circular metallic frame. The frame is concentric and coplanar with the orbit. The radius of the frame is now gradually decreased. Assuming that the particle remains within the frame at all times, what changes to the trajectory of the particle will occur as the frame is being shrunk?