Cathode rays travelling from east to west enter into region of electric field directed towards north to south in the plane of paper. The deflection of cathode rays is towards

A charged particle (mass $m$ and charge $q$ ) moves along $X$ axis with velocity $V _{0}$. When it passes through the origin it enters a region having uniform electric field $\overrightarrow{ E }=- E \hat{ j }$ which extends upto $x = d$. Equation of path of electron in the region $x > d$ is 

A mass $m = 20\,g$ has a charge $q = 3.0\,mC$. It moves with a velocity of $20\,m/s$ and enters a region of electric field of $80\,N/C$ in the same direction as the velocity of the mass. The velocity of the mass after $3$ seconds in this region is.......$m/s$

An electron enters a parallel plate capacitor with horizontal speed $u$ and is found to deflect by angle $\theta$ on leaving the capacitor as shown below. It is found that $\tan \theta=0.4$ and gravity is negligible. If the initial horizontal speed is doubled, then the value of $\tan \theta$ will be

A charged particle of mass $m = 2\ kg$ and charge $1μC$ is projected from a horizontal ground at an angle $\theta  = 45^o$ with speed $10\ ms^{-1}$ . In space, a horizontal electric field towards the direction of projection $E = 2 \times 10^7\ NC^{-1}$ exists. The range of the projectile is......$m$

The electric field inside a spherical shell of uniform surface charge density is