List of practice Questions

An electron moving with the speed $5 \times 10^{6}$ per sec is shooted parallel to the electric field of intensity $1 \times 10^{3} \,N / C$. Field is responsible for the retardation of motion of electron. Now evaluate the distance travelled by the electron before coming to rest for an instant (mass of $e=9 \times 10^{-31} \,kg$, charge $\left.=1.6 \times 10^{-19} \,C \right)$

Let $E_{a}$ be the electric field due to a dipole in its axial plane distant $1$ and let $E _{ q }$ be the field in the equitorial plane distant $1 '$. The relation between $E _{ a }$ and $E _{q}$ is

Two point charges $-q$ and $+q/2$ are situated at the origin and at the point $(a, 0, 0)$ respectively. The point along the $X$-axis where the electric field vanishes is

Two identical conducting balls $A$ and $B$ have positive charges $q_1$ and $q_2$ respectively but $q_1 \ne q_2$ The balls are brought together so that they touch each other and then kept in their original positions. the force between them is

The electric flux for Gaussian surface $A$ that encloses the charged particles in free is (Given $q_1, = - 14 \, n \, C, q_2 = 78.85 \, n \, C, \, q_3 = - 56 \, n \, C) $

Electric field produced by an electron at a point is $E$. What will be electric field produced by $Li^{+++}$ at the same point if it is placed at position of electron ?

Let there be a spherically symmetric charge distribution with charge density varying as $\rho\left(r\right) = \rho_{0} \left(\frac{5}{4}-\frac{r}{R}\right)$ upto $r = R$, and $\rho \left(r\right) = 0$ for $r > R$, where r is the distance from the origin. The electric field at a distance $r\left(r < R\right)$ from the origin is given by

Two charged spherical conductors of radii $ {{R}_{1}} $ and $ {{R}_{2}} $ are connected by a wire. Then the ratio of surface charge densities of the spheres $ {{\sigma }_{1}}/{{\sigma }_{2}} $ is

Let $ f : R $ - { $ \frac {5}{4} $ } $ \rightarrow R $ be a function defined as $ f(x) = \frac{5x}{4x+5} $ . The inverse of $ f $ is the map $ g : Range\,f\,\rightarrow R $ - { $ \frac {5}{4} $ } given by

Let $ * $ be a binary operation on the set $ Q $ of rational numbers defined by $ a*b $ = $ \frac{ab}{4} $ . The identity with respect to this operation is

With the increase of temperature, the surface tension of the liquid

In a homonuclear molecule, which of die following sets of orbitals is degenerate?

For the equations $ x + 2y + 3z = 1 $ , $ 2x + y + 3z = 2 $ , $ 5x + 5y + 9z = 4 $

The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system A $\begin {bmatrix} x \\ y \\ z \end {bmatrix}-\begin {bmatrix} 1 \\ 0 \\ 0 \end {bmatrix}$ has exactly two distinct solutions, is

If $B$ is a non-singular matrix and $A$ is a square matrix, then det $(B^{-1} AB)$ is equal to

Let A be a $2 \times 2$ matrix with non-zero entries and let $A^2 = I$, where I is $2 \times 2$ identity matrix. Define Tr(A) = sum of diagonal elements of A and $|A|$ = determinant of matrix A. $Tr(A) = 0$ $|A| = 1$

Consider the system of linear equations; $x_1 + 2x_2 + x_3 = 3$ $2x_1 + 3x_2 + x_3 = 3$ $3x_1 + 5x_2 + 2x_3 = 1 $ The system has

The kinetic energy of an electron, which is accelerated in the potential difference of 100 V, is

Figure shows three spherical and equipotential surfaces A, B and C round a point charge The potential difference $V_A - V_B = V_B - V_C. \, If \, t_1 \, and \, t_2$ be the distances between them, then

A slab of material of dielectric constant $K$ has the same area as the plates of a parallel plate capacitor but has a thickness $\left(\frac{3}{4}\right) d$, where $d$ is the separation of the plates. The ratio of the capacitance $C$ (in the presence of the dielectric) to the capacitance $C_{0}$ (in the absence of the dielectric) is

The effective capacitance between $A$ and $B$ is

An $8\, \mu F$ capacitor is connected across $220\,V, 50 \,Hz $ line. What is the peak value of the charge through capacitor?

0.2 F capacitor is charge to 600 V by a battery, on removing the battery, it is connected with another parallel plate condenser of I F . The potential decreases to

An uncharged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of $V_0$. lf the common potential after sharing of charges becomes V, then the dielectric constant of the dielectric must be

Two point-charges $ \pm 10\mu C $ are placed $ 5.00\,mm $ apart, forming an electric dipole. Compute electric field at a point on the axis of the dipole $ 15\,cm $ away from the centre on a line passing through the centre dipole.