Electric Charges and Fields — Class 12 Physics PYQs

Figure shows variation of Coulomb force (F) acting between two point charges with $1/r^2$, r being the separation between the two charges ($q_1,q_2$) and ($q_2,q_3$). If $q_2$ is positive and least in magnitude, then the magnitudes of $q_1,q_2$ and $q_3$ are such that
(A) $q_2<q_3<q_1$
(B) $q_3<q_1<q_2$
(C) $q_1<q_2<q_3$
(D) $q_2<q_1<q_3$

Two identical point charges are placed at the two vertices A and B of an equilateral triangle ABC. If M is the mid-point of AB, the net electric field at C will point along
(A) CA
(B) CB
(C) MC
(D) CM

Which one of the following statements is correct ?
Electric field due to static charges is
(A) conservative and field lines do not form closed loops.
(B) conservative and field lines form closed loops.
(C) non-conservative and field lines do not form closed loops.
(D) non-conservative and field lines form closed loops.

In a region of a uniform electric field $\vec{E}$, a negatively charged particle is moving with a constant velocity $\vec{v}=-v_0\hat{i}$ near a long straight conductor coinciding with XX' axis and carrying current I towards -X axis. The particle remains at a distance d from the conductor.
(i) Draw diagram showing direction of electric and magnetic fields.
(ii) What are the various forces acting on the charged particle ?
(iii) Find the value of $v_0$ in terms of E, d and I.

Two point charges $5\mu C$ and $-1\mu C$ are placed at points $(-3cm,0,0)$ and $(3cm,0,0)$ respectively. An external electric field $\vec{E}=\frac{A}{r^2}\hat{r}$ where $A=3\times 10^5$ Vm is switched on in the region. Calculate the change in electrostatic energy of the system due to the electric field.

A thin plastic rod is bent into a circular ring of radius R. It is uniformly charged with charge density $\lambda$. The magnitude of the electric field at its centre is :
(A) $\frac{\lambda }{2{ϵ}_{0}R}$
(B) Zero
(C) $\frac{\lambda }{4\pi {ϵ}_{0}R}$
(D) $\frac{\lambda }{4{ϵ}_{0}R}$

Two charged particles P and Q, having the same charge but different masses m${}_P$ and m${}_Q$, start from rest and travel equal distances in a uniform electric field $\vec{E}$ in time t${}_P$ and t${}_Q$ respectively. Neglecting the effect of gravity, the ratio $\frac{t_P}{t_Q}$ is :
(A) $\sqrt{\frac{m_P}{m_Q}}$
(B) $\sqrt{\frac{m_Q}{m_P}}$
(C) $\frac{m_P}{m_Q}$
(D) $\frac{m_Q}{m_P}$

Three small charged spheres X, Y and Z carrying charges + q, – q and + q respectively are placed equidistant from each other, as shown in the figure. The spheres Y and Z are held in place. Initially X is also held in place, but is otherwise free to move. When X is released, the path followed by it will be :
(A) A
(B) B
(C) C
(D) D

A cube of side 0.1 m is placed, as shown in the figure, in a region where electric field $\vec{E}=500x\hat{i}$ exists. Here x is in meters and E in NC${}^{-1}$. Calculate :
(a) the flux passing through the cube, and
(b) the charge within the cube.

Derive an expression for potential energy of an electric dipole $\vec{p}$ in an external uniform electric field $\vec{E}$. When is the potential energy of the dipole (1) maximum, and (2) minimum ?
(ii) An electric dipole consists of point charges – 1.0 pC and + 1.0 pC located at (0, 0) and (3 mm, 4 mm) respectively in x – y plane. An electric field $\vec{E}=\left(\frac{1000\text{V}}{\text{m}}\right)\hat{i}$ is switched on in the region. Find the torque $\vec{\tau }$ acting on the dipole.
OR
(b) (i) An electric dipole (dipole moment $\vec{p}=p\hat{i}$), consisting of charges – q and q separated by distance 2a, is placed along the x-axis, with its centre at the origin. Show that the potential V, due to this dipole, at a point x, (x >> a) is equal to $\frac{1}{4\pi {ϵ}_0}\cdot \frac{p\cdot \hat{i}}{x^2}$.
(ii) Two isolated metallic spheres S${}_1$ and S${}_2$ of radii 1 cm and 3 cm respectively are charged such that both have the same charge density $\left(\frac{2}{\pi }\times 10^{-9}\right){\text{C/m}}^2$. They are placed far away from each other and connected by a thin wire. Calculate the new charge on sphere S${}_1$.