Electric Charges and Fields Set-2

Q1. (Two point charges $+3q$ and $+q$ are fixed on the $x$‑axis at $x=0$ and $x=12\ \text{cm}$ respectively. Let $P$ be a point on the line joining them where the net electric field is zero. The coordinate of $P$ measured from the charge $+3q$ is closest to:)

Q2. (Assertion (A): For an isolated metallic conductor in electrostatic equilibrium all excess charge resides entirely on its outer surface.
Reason (R): The electric field at points outside a uniformly charged spherical shell is identical to that produced by a point charge placed at its centre.)

Q3. (A solid insulating sphere of total charge $Q$ and radius $R$ has charge distributed uniformly throughout its volume. Using the known behaviour $E\propto r$ for $r<R$ and $E\propto 1/r^2$ for $r>R$, the ratio $\dfrac{E(r=R/2)}{E(r=2R)}$ equals:)

Q4. (A neutral hollow conducting spherical shell initially isolated has a point charge $+q$ placed at the geometric centre of its cavity. The shell is then connected to earth (grounded) and after electrostatic equilibrium is reached the ground connection is removed while the point charge $+q$ remains inside. The net charge on the conductor and the electric field outside the shell respectively are:)

Q5. (Assertion (A): In electrostatic equilibrium the electric field inside the bulk of a conductor is zero.
Reason (R): Hence the electric potential everywhere inside the conductor must be zero.)

Q6. A spherically symmetric charge distribution produces an electric field of magnitude

where $E(R)=E_0$. The electric potential at the centre relative to infinity, $V(0)$, equals:

Q7. (A dipole consists of charges $+q$ at $x=+d/2$ and $-q$ at $x=-d/2$ (so dipole moment $p=qd$) and is centered at the origin along the $x$‑axis. It is placed in an external electric field $E(x)=E_0+\alpha x$ (with $\alpha$ constant). To first order in $d$ the net force on the dipole is:)

Q8. (Assertion (A): If the total charge enclosed by a Gaussian surface is zero, then the electric field must be zero everywhere on that surface.
Reason (R): Gauss's law states that the net flux through a closed surface equals the enclosed charge divided by $\varepsilon_0$.)

Q9. (A point charge $q=2.0\ \mu\text{C}$ is held at a distance $a=0.10\ \text{m}$ above an infinite grounded conducting plane in vacuum. Using the method of images, the magnitude of the electrostatic force on $q$ is approximately:)

Q10. (A ring of radius $R$ carries total charge $Q$ uniformly distributed. The axial field at a distance $z$ from the centre is

For $z>0$ the value of $z$ at which $|E(z)|$ is maximum is:)