Physics Electric Charge and Field

Given below are two statements:

Statement I : The electric force changes the speed of the charged particle and hence charges its kinetic energy; whereas the magnetic force does not change like kinetic energy of the charged particle.

Statement II : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerated the moving charged particle along the direction of magnetic field.

In the light of the above statements, chose the most appropriate answer from the option given below

A running fork of frequency 340 Hz resonates in the fundamental mode with a air column of length 125cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is __________cm.

(Velocity of sound in air is 340 ms^-1)

A capacitor C₁ of capacitance $5\mu F$  is charged to a potential of 30V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C₂ of capacitance $10\mu F$ as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C₂ is__________   $\mu C.$

In the following unclear reaction,

           D   $\stackrel{\alpha }{\to }{D}_1\stackrel{{\beta }^{-}}{\to }{D}_2\stackrel{\alpha }{\to }{D}_3\stackrel{\gamma }{\to }{D}_4$

           Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D₄ respectively will be________

Two point charges A and B of magnitude + 8 * 10^-6 and -8 * 10^-6C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 * 10⁴ NC^-1. The distance 'd' between the point charges A and B is:

Two point charges A and B of magnitude + 8 * 10^-6 and -8 * 10^-6C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 * 10⁴ NC^-1. The distance 'd' between the point charges A and B is:

Three point charges of magnitude $5\mu C,0.16\mu C,and0.3\mu C$ are located at the vertices A, B, C of a right angled triangle whose sides are AB = 3cm, BC = $3\sqrt[]{2}$ and CA = 3 and point A is the right angle corner. Charge at point A experiences __________ N of electrostatic force due to the other two charges.

A particle of charge $q$ and mass $m$ is subjected to an electric field $E=E_0\left(1-a{x}^2\right)$ in the $\mathrm{x}$ -direction, where $a$ and ${\mathrm{E}}_0$ are constants. Initially the particle was at rest at $\mathrm{x}=0$ . Other then the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is: