The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor
The magnitude of electric field $E$ in the annular region of a charged cylindrical capacitor
- [IIT 1996]
- A
Is same throughout
- B
Is higher near the outer cylinder than near the inner cylinder
- C
Varies as $1/r$, where $r$ is the distance from the axis
- D
Varies as $1/{r^2}$, where $r$ is the distance from the axis
Similar Questions
Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.
Reason $R:$ Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below.
Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.
Reason $R:$ Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below.
- [JEE MAIN 2023]
Answer the following:
$(a)$ The top of the atmosphere is at about $400\; kV$ with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about $100\; Vm ^{-1} .$ Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
$(b)$ A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area $1\; m ^{2} .$ Will he get an electric shock if he touches the metal sheet next morning?
$(c)$ The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \;A$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?
$(d)$ What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning? (The earth has an electric field of about $100\; Vm ^{-1}$ at its surface in the downward direction, corresponding to a surface charge density $=-10^{-9} \;C \,m ^{-2} .$ Due to the slight conductivity of the atmosphere up to about $50\; km$ (beyond which it is good conductor), about $+1800 \;C$ is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.)
Answer the following:
$(a)$ The top of the atmosphere is at about $400\; kV$ with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about $100\; Vm ^{-1} .$ Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
$(b)$ A man fixes outside his house one evening a two metre high insulating slab carrying on its top a large aluminium sheet of area $1\; m ^{2} .$ Will he get an electric shock if he touches the metal sheet next morning?
$(c)$ The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \;A$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words, what keeps the atmosphere charged?
$(d)$ What are the forms of energy into which the electrical energy of the atmosphere is dissipated during a lightning? (The earth has an electric field of about $100\; Vm ^{-1}$ at its surface in the downward direction, corresponding to a surface charge density $=-10^{-9} \;C \,m ^{-2} .$ Due to the slight conductivity of the atmosphere up to about $50\; km$ (beyond which it is good conductor), about $+1800 \;C$ is pumped every second into the earth as a whole. The earth, however, does not get discharged since thunderstorms and lightning occurring continually all over the globe pump an equal amount of negative charge on the earth.)
Two capacitors $C_1$ and $C_2$ are charged to $120\ V$ and $200\ V$ respectively. It is found that connecting them together the potential on each one can be made zero. Then
Two capacitors $C_1$ and $C_2$ are charged to $120\ V$ and $200\ V$ respectively. It is found that connecting them together the potential on each one can be made zero. Then
- [JEE MAIN 2013]
The capacitance of a spherical condenser is $1\,\mu F$. If the spacing between the two spheres is $1\,mm$, then the radius of the outer sphere is
The capacitance of a spherical condenser is $1\,\mu F$. If the spacing between the two spheres is $1\,mm$, then the radius of the outer sphere is
The distance between the circular plates of a parallel plate condenser $40\,mm$ in diameter, in order to have same capacity as a sphere of radius $1\;metre$ is....$mm$
The distance between the circular plates of a parallel plate condenser $40\,mm$ in diameter, in order to have same capacity as a sphere of radius $1\;metre$ is....$mm$