Q. Two uniformly long charged wires with linear densities $\lambda $ and $3 \lambda $ are placed along $X$ and $Y$ axis respectively. Determined the slope of electric field at any point on the line $y=\sqrt{3} \, x$ .

NTA AbhyasNTA Abhyas 2022Electrostatic Potential and Capacitance Report Error

A

$3\sqrt{3}$

B

$\frac{\sqrt{3}}{3 \sqrt{2}}$

C

$\frac{1}{3 \sqrt{3}}$

D

$\sqrt{3}$

Solution:

$E_{x}=\frac{3 \lambda }{2 \pi ϵ_{o} x}$
$E_{y}=\frac{\lambda }{2 \pi ϵ_{o} x \sqrt{3}}$
$\overset{ \rightarrow }{E}=\frac{3 \lambda }{2 \pi ε_{0} x}\hat{i}+\frac{\lambda }{2 \pi ε_{0} x \sqrt{3}}\hat{j}$
$Slope=\frac{E_{y}}{E_{x}}=\frac{\lambda /2 \pi \epsilon _{0} \sqrt{3} x}{3 \lambda /2 \pi \epsilon _{0} x}=\frac{1}{3 \sqrt{3}}$

Questions from NTA Abhyas 2022

1. A thin semicircular conducting ring of the radius $R$ is falling with its plane vertical in a horizontal magnetic induction $\overset{ \rightarrow }{B}$ . At the position MNQ, the speed of the ring is $v$ and the potential difference developed across the ring is

2. An ideal gas at $27 \, ^\circ C$ is compressed adiabatically to $8/27$ of its original volume. If $\gamma =5/3$ , then the rise in temperature is

3. Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?

4. Two perfectly elastic objects $A$ and $B$ of identical mass are moving with velocities $15 \, m \, s^{- 1}$ and $10 \, m \, s^{- 1}$ respectively, collide along the direction of line joining them. Their velocities after the collision are respectively

5. The force of repulsion between two point charges is $F$ , when these are at distance $0.5 \, m$ apart. Now the point charges are replaced by non conducting spheres of radii $5 \, cm$ each having the same charge as that of the respective point charges. The distance between their centres is again kept $0.5m.$ Then the force of repulsion will

Electrostatic Potential and Capacitance

Questions from Electrostatic Potential and Capacitance

1. In the adjoining figure, the electric field lines for charges $q_{1}$ and $q_{2}$ are shown. Identify the sign of the charges.

NTA Abhyas 2020

2. A charge $Q$ is distributed over two concentric conducting thin spherical shells radii $r$ and $R$ $( R > r )$. If the surface charge densities on the two shells are equal, the electric potential at the common centre is :

JEE Main 2020

3. A little charged bead is inside the hollow frictionless sphere manufactured from the insulating material. Sphere has a diameter of $50 \, cm$ . The mass of the bead is $90 \, mg$ , its charge is $0.5\text{ μC}$ . What minimum charge must carry an object at the bottom of the sphere to keep hold the charged bead at the vertex of the sphere in stable equilibrium?

NTA Abhyas 2020

4. The capacitance of an air capacitor is $15\, \mu F$ the separation between the parallel plates is $6\, mm$. A copper plate of $3\, mm$ thickness is introduced symmetrically between the plates. The capacitance now becomes

5. Three capacitors of $2.0\, \mu F ,\, 3.0\, \mu F$ and $6.0\, \mu F$ are connected in series to a $10\, V$ source. The charge on the $3.0\, \mu F$ capacitor is

Physics Most Viewed Questions

1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

NEET 2021 Physical World, Units and Measurements

2. The de Broglie wavelength of an electron moving with kinetic energy of $144 \,eV$ is nearly

NEET 2020 Dual Nature of Radiation and Matter

3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

NEET 2021 Motion in a Straight Line

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

NEET 2020 Electromagnetic Induction

5. A barometer is constructed using a liquid (density $= 760 \,kg/m^{3})$ What would be the height of the liquid column, when a mercury barometer reads $76\, cm$ ?
(density of mercury $= 13600 kg/m^{3})$

NEET 2020 Mechanical Properties of Fluids