A charged particle is projected with a velocity $v$ at an angle $heta$ to a uniform electric field $E$. If the particle's velocity becomes perpendicular to the field after time $t$, then what is the initial velocity component perpendicular to the field?

A toy car experiences a constant acceleration in a straight line, changing its velocity from $4 \, m/s$ to $10 \, m/s$ in $2 \, s$. At this point, the acceleration reverses direction, and the car's velocity returns to $4 \, m/s$ after another $2 \, s$. Determine the car's average speed and average velocity over these $4 \, s$.

Two identical charged spheres of mass $m$ and charge $q$ are suspended from the same point by insulating threads of length $L$. The spheres repel each other and come to equilibrium separated by a distance $d$. What is the magnitude of the charge $q$ on each sphere?

Two identical charged particles are projected into a uniform electric field. Particle A is projected at an angle $heta$ with the field, while particle B is projected perpendicular to the field. If both have the same initial kinetic energy, which particle will have a greater range along the direction of the field?

n identical mercury droplets charged to the same potential $V$ coalesce to form a single bigger drop. The potential of new drop will be

A point charge $7.5\mu C$ is kept at the origin. The magnitude of strength of electric field at (4m, 3m) is

An electron enters in high potential region ${V_2}$ from lower potential region ${V_1}$ then its velocity

An electron falls from rest through a vertical distance ${\rm{h}}$ in a uniform and vertically upward directed electric field ${\rm{E}}$.The direction of electric field is not reversed, keeping its magnitude the same. A proton is allowed to fall from rest inits through the same vertical distance ${\rm{h}}$. the time of fall of the electron, in comparison to the time of fall of the protonof

A charged particle of mass $5 imes {10^{ - 5}}kg$ is held stationary in space by placing it in an electric field of strength ${10^7}N{C^{ - 1}}$ directed vertically downwards. The charge on the particle is

Two small, equally charged water droplets are suspended in air by thin threads of equal length. They repel each other and are a distance $d$ apart. Due to evaporation, the charges on the droplets decrease at a constant rate. As they move closer, their velocity $v$ depends on their separation $x$. What is the relationship between $v$ and $x$?

When a proton is accelerated through $1V,$ then its kinetic energy will be