The given diagram shows two semi infinite line of charges having equal (in magnitude) linear charge density but with opposite sign. The electric field at any point on $x$ axis for $(x > 0)$ is along the unit vector

How many electrons should be removed from a coin of mas $1.6 \,g$, so that it may float in an electric field of intensity $10^9 \,N / C$ directed upward?

An oil drop of $12$ excess electrons is held stationary under a constant electric field of $2.55 \times 10^{4}\; N\,C ^{-1}$ (Millikan's oil drop experiment). The density of the oil is $1.26 \;g \,cm ^{-3} .$ Estimate the radius of the drop. $\left(g=9.81\; m s ^{-2} ; e=1.60 \times 10^{-19}\; \,C \right)$

Deutron and $\alpha - $ particle are put $1\,\mathop A\limits^o $ apart in air. Magnitude of intensity of electric field due to deutron at $\alpha - $ particle is

Two charges each equal to $\eta q({\eta ^{ - 1}} < \sqrt 3 )$ are placed at the corners of an equilateral triangle of side $a$. The electric field at the third corner is ${E_3}$ where $({E_0} = q/4\pi {\varepsilon _0}{a^2})$

Charges $Q _{1}$ and $Q _{2}$ arc at points $A$ and $B$ of a right angle triangle $OAB$ (see figure). The resultant electric field at point $O$ is perpendicular to the hypotenuse, then $Q _{1} / Q _{2}$ is proportional to