Q. An electric field $\vec{E}=\left(25 \hat{i}+30 \hat{j}\right)NC^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x = 2\, m$, $y = 2\, m$ is ;

JEE MainJEE Main 2015Electrostatic Potential and Capacitance Report Error

A

$-130 V$

4%

B

$-120 V$

8%

C

$-140 V$

7%

D

$-110 V$

81%

Solution:

$\Delta V=-\int_\limits{A}^{B} \vec{E} \cdot d \bar{r}$
$=-\int(25 i+30 j) \cdot(dxi +dyj)$
$\Rightarrow V_{B}-V_{A}=-\int 25 d x+30 d y$
$\Rightarrow V_{B}=-25(x)_{0}^{2}-30(y)_{0}^{2}=-50-60=-110\, V$

Questions from JEE Main 2015

1. The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{\frac{L}{g}}$. Measured value of $L$ is $20.0\, cm$ known to $1\, mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\, s$ using a wrist watch of $1\, s$ resolution. The accuracy in the determination of $g$ is

Physical World, Units and Measurements

2. The current voltage relation of diode is given by $I=\left(e^{1000 V / T}-1\right) mA$, where the applied voltage $V$ is in volt and the temperature $T$ is in kelvin. If a student makes an error measuring $\pm 0.01\, V$ while measuring the current of $5 \,mA$ at $300 \,K$, what will be the error in the value of current in $mA$ ?

Physical World, Units and Measurements

3. Distance of the centre of mass of a solid uniform cone from its vertex is $z_0$ If the radius of its base is $R$ and its height is $h$, then $z_0$ is equal to

System of Particles and Rotational Motion

4. A particle of mass $m$ moving in the $x$-direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$-direction with speed $v$. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

Work, Energy and Power

5. A train is moving on a straight track with speed $20\, ms^{-1}.$ It is blowing its whistle at the frequency of $1000\, Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is close to (speed of sound $= 320\,ms^{-1}$)

Waves

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