Electric Charges and Fields Set-4

Q1. Three identical point charges $q$ are placed at three vertices of a square of side $a$ (one vertex is empty). What is the magnitude of the resultant electric field at the centre of the square?

Q2. A point charge $q$ is placed at the centre of an isolated thin conducting spherical shell of radius $R$ which carries an excess charge $Q$. For $r>R$, the magnitude of electric field at distance $r$ from the centre is:

Q3. Three identical charges $+q$ are fixed at the vertices of an equilateral triangle of side $a$. A fourth charge $+2q$ is brought from infinity and placed at the centroid. The work done by external agent (quasi-statically) in assembling this charge at the centroid is:

Q4. A uniformly charged thin ring of radius $R$ and total charge $Q$ produces on its axis an axial field $E(x)=\dfrac{1}{4\pi\epsilon_{0}}\dfrac{Qx}{(x^{2}+R^{2})^{3/2}}$. For $x>0$, the value of $x$ at which $E(x)$ is maximum is:

Q5. Assertion (A): The electric field inside the hollow cavity of an isolated conductor is zero when there are no charges in the cavity and only external charges are present. Reason (R): Free charges in the conductor redistribute to the outer surface so as to cancel any field produced by external charges inside the cavity.

Q6. Two equal positive point charges $+Q$ are placed at $x=+a$ and $x=-a$. At the origin:

Q7. A dipole consists of charges $+q$ at $x=+a$ and $-q$ at $x=-a$. At a point $P$ on the positive $y$–axis $(0,y)$ with $y>a$, which of the following is true?

Q8. A point charge $q$ is held at distance $d$ from a grounded infinite conducting plane. The magnitude of the attractive force exerted by the plane on the charge is:

Q9. The radial electric field of a spherically symmetric charge distribution is plotted as $E(r)\propto r$ for $r\le R$ and $E(r)\propto 1/r^{2}$ for $r\ge R$. Which statement about the volume charge density $\rho(r)$ for $r<R$ is correct?

Q10. Two point charges $+Q$ and $+4Q$ are fixed at $x=0$ and $x=d$ respectively. At the point $x=\dfrac{d}{3}$ (between them) the net electric field is zero. The electric potential at that point equals: