Introducing Epsilon

Q. Two charges $q_1$ and $q_2$ are placed in vacuum at a distance d and the force acting between them is F. If a medium of dielectric constant 4 is introduced around them, the force now will be

1. $4F$
2. $2F$
3. $\frac{F}{2}$
4. $\frac{F}{4}$

Q. Dielectric constant of pure water is 81. Its permittivity will be

1. $8.86\times {10}^{-12}MKSunits$
2. $1.02\times {10}^{13}MKSunits$
3. Cannot be calculated
4. $7.12\times {10}^{-10}MKSunits$

Q.

Two charges q and -3q are placed fixed on x-axis separated by distance d. At what distance from the q should a third charge 2q be placed such that it will not experience any force?

1. $\frac{d+\sqrt{3}d}{2}$
2. $\frac{d+3d}{2}$
3. $\frac{d-3d}{2}$
4. $\frac{d-\sqrt{3}d}{2}$

Q.

Two charges placed in air repel each other by a force of ${10}^{N}N.$ When oil is introduced between the charges, the force becomes $2.5\times {10}^{-5}N$. The dielectric constant of oil is

1. 2.5

2. 0.25

3. 2.0

4. 4.0

Q.

What does dielectric strength mean?

Q. The ratio of the forces between two small spheres with constant charge (a) in air (b) in a medium of dielectric constant K is

1. $1:K^2$
2. $K^2:1$
3. 1 : K
4. K : 1

Q.

Show that 1C = 3*10⁹Stat c

Q.

What is the effect of temperature on dielectric constant?

Q.

At room temperature, if the relative permittivity of water is $80$ and the relative permeability be $0.0222$ then the velocity of light in water is ____________$\mathrm{m}/\mathrm{s}$

1. $2.5\times {10}^8$

2. $2.25\times {10}^8$

3. $3.5\times {10}^8$

4. $3\times {10}^8$

Q. With the rise in temperature, the dielectric constant K of a liquid

1. Decreases
2. Remains unchanged
3. Charges erratically
4. Increases

Q. Four identical point masses, each of mass m and carrying charge +q are placed at the corners of a square of sides 'a' on a frictionless plain surface. If the particles are released simultaneously, the kinetic energy of the system when they are infinitely far apart is

1. $\frac{q^2}{4\pi {ϵ}_{0}a}(2\sqrt{2}+1)$
2. $\frac{q^2}{4\pi {ϵ}_{0}a}(\sqrt{2}+2)$
3. $\frac{q^2}{4\pi {ϵ}_{0}a}(\sqrt{2}+4)$
4. $\frac{q^2}{4\pi {ϵ}_{0}a}(\sqrt{2}+1)$

Q. Five charges of equal values placed at cornersof a regular pentagon of side a. The force onwhich is placed at centroid O is

Q. For a series LCR circuit, the power dissipated at resonance is (symbols have their usual meaning) ($I$ : rms current)

1. $\frac{V^2}{(X_L-X_C)}$
2. $I^2\omega L$
3. $I^{2}R$
4. $I^2(X_L-X_C)$

Q. A parallel plate capacitor having an area A and separated by a distance d is filled by a copper plate of area A and thickness b. The new capacitance is:

1. $\frac{{\epsilon }_{0}A}{d-\frac{b}{2}}$
2. $\frac{{\epsilon }_{0}A}{2d}$
3. $\frac{{\epsilon }_{0}A}{d+\frac{b}{2}}$
4. $\frac{{\epsilon }_{0}A}{d-b}$

Q.

Electric current has both magnitude and direction . But still , it is referred to as a scalar quantity. I mean, how's that possible??!!

Q. 96.a wire of linear charge density lemdaa passes through a cuboid of length L , breadth B and height H in such a manner that flux through the cuboid is maximum . The position of wire is now changed . so that the flux through the cuboid is minimum . L > B > H , then the ratio of maximum flux to minimum flux will be

Q.

How do you calculate capacitance with two dielectrics?

Q.

Why do dielectrics increase capacitance ?

Q.

If ${ϵ}_{0}and{\mu }_0$ are the permittivity and permeability of free space and $ϵand\mu$ are the corresponding quantities for a medium, Then refractive index of the medium is

1. $1$

2. $\sqrt{\frac{{\mu }_0{ϵ}_0}{\mu ϵ}}$

3. $Insufficientinformation$

4. $\sqrt{\frac{\mu ϵ}{{\mu }_0{ϵ}_0}}$

Q.

Two charged spheres separated at a distance d exert a force F on each other. If they are immersed in a liquid of dielectric constant 2, then what is the force (if all conditions are same)

1. F
   
2. 2F
3. 4F
4. $\frac{F}{2}$
   

Q.

If $n,e,\tau$ and $m$, are representing electron density charge, relaxation time, and mass of an electron respectively then the resistance of a wire of length l and cross-sectional area A is given by

1. $\raisebox{1ex}{$ml$}\!\left/ \!\raisebox{-1ex}{$n{e}^2\tau A$}\right.$

2. $\raisebox{1ex}{$2mA$}\!\left/ \!\raisebox{-1ex}{$n{e}^2\tau $}\right.$

3. $n{e}^2\tau A$

4. $\raisebox{1ex}{$n{e}^2\tau A$}\!\left/ \!\raisebox{-1ex}{$2m$}\right.$

Q. 40.The average value of sawtooth voltage V=V^°{2t/T-1} over 0 to T/2 is given by

Q. The distance between the plates of a parallel plate capacitor is $0.05\text{m}$. An electric field of magnitude $3\times {10}^4\text{V/m}$ is established between the plates by connecting it to a battery. It is disconnected from the battery and an uncharged plate of thickness $0.01\text{m}$ and dielectric constant $k=2$ is inserted then, what will be the magnitude of difference in potential difference (in $\text{kV}$) between plates?

Q.

If resistivity of pure silicon is $3000\Omega m$ and the electron and hole mobilities are $0.12m^2{v}^{-1}{s}^{-1}$ and $0.045m^2{v}^{-1}{s}^{-1}$ respectively. Determine the resistivity of a specimen of the material when ${10}^{19}$ atoms of phosphorous are added per $m^3$ Given e= $1.6\times {10}^{-19}C$, $p=3000\Omega$, ${\mu }_e=0.12m^2{v}^{-1}{s}^{-1}$, ${\mu }_h=0.045m^2{v}^{-1}{s}^{-1}.$

Q. $\text{Statement 1:}$ Increasing the charge on the plates of a capacitor increases its capacitance.

$\text{Statement 2:}$ Because $Q=CV$, implies $Q$ is proportional to $C$.

1. Statement $1$ is right and statement $2$ is wrong.
2. Both the statements are right.
3. Statement $1$ is wrong and statement $2$ is right.
4. Both the statements are wrong.

Q. 18. In an inductor, the current / varies with time tas {1=5A+16(A/s)t . If induced emf in the inductor { is 5mV , the self inductance of the inductor is { (1) 3.75×10^{-3H (2) 3.75×10^{-4H{ (3) 3.125×10^{-3H (4) 3.125×10^{-4H

Q.

Is the capacitor linear or nonlinear?

Q. The plates of a parallel plate capacitor have an area of $90c{m}^2$ each and are separated by $2mm$. The capacitor is charged by connecting it to a $400V$ supply. Then the energy density of the energy stored $\left(inJ{m}^{-3}\right)$ in the capacitor is (Take ${ϵ}_0=8.8\times {10}^{-12}F{m}^{-1}$)

1. $0.113$
2. $0.117$
3. $0.152$
4. $\text{None of these}$

Q. The intensity of electric field at a point between the plates of a charged capacitor

1. Is directly proportional to the distance between the plates
2. Is inversely proportional to the distance between the plates
3. Is inversely proportional to the square of the distance between the plates
4. Does not depend upon the distance between the plates

Q.

A parallel plate condenser is filled with two dielectrics as shown.


Area of each plate is $A$ $m^2$ and the separation is $t$ m. The dielectric constants are $k_1$ and $k_2$ respectively. Its capacitance in farad will be

1. $\frac{{\epsilon }_{o}A}{2t}(k_1+k_2)$
2. $\frac{{\epsilon }_{o}A}{t}(k_1+k_2)$
3. $\frac{{\epsilon }_{o}A}{2t}(k_1-k_2)$
4. $\frac{2{\epsilon }_{o}A}{t}(k_1+k_2)$