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
Capacitance (in $F$) of a spherical conductor with radius $1\, m$ is
Capacitance (in $F$) of a spherical conductor with radius $1\, m$ is
- [AIEEE 2002]
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.)
Sixty-four drops are jointed together to form a bigger drop. If each small drop has a capacitance $C$, a potential $V$, and a charge $q$, then the capacitance of the bigger drop will be
Sixty-four drops are jointed together to form a bigger drop. If each small drop has a capacitance $C$, a potential $V$, and a charge $q$, then the capacitance of the bigger drop will be
A $500\,\mu F$ capacitor is charged at a steady rate of $100\,\mu C/sec$ . The potential difference across the capacitor will be $10\,V$ after an interval of......$sec$
A $500\,\mu F$ capacitor is charged at a steady rate of $100\,\mu C/sec$ . The potential difference across the capacitor will be $10\,V$ after an interval of......$sec$
Answer carefully:
$(a)$ Two large conducting spheres carrying charges $Q _{1}$ and $Q _{2}$ are brought close to each other. Is the magnitude of electrostatic force between them exactly given by $Q _{1} Q _{2} / 4 \pi \varepsilon_{0} r^{2},$ where $r$ is the distance between their centres?
$(b)$ If Coulomb's law involved $1 / r^{3}$ dependence (instead of $1 / r^{2}$ ), would Gauss's law be still true?
$(c)$ $A$ small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
$(d)$ What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?
$(e)$ We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?
$(f)$ What meaning would you give to the capacitance of a single conductor?
$(g)$ Guess a possible reason why water has a much greater dielectric constant $(=80)$ than say, mica $(=6)$
Answer carefully:
$(a)$ Two large conducting spheres carrying charges $Q _{1}$ and $Q _{2}$ are brought close to each other. Is the magnitude of electrostatic force between them exactly given by $Q _{1} Q _{2} / 4 \pi \varepsilon_{0} r^{2},$ where $r$ is the distance between their centres?
$(b)$ If Coulomb's law involved $1 / r^{3}$ dependence (instead of $1 / r^{2}$ ), would Gauss's law be still true?
$(c)$ $A$ small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point?
$(d)$ What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical?
$(e)$ We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?
$(f)$ What meaning would you give to the capacitance of a single conductor?
$(g)$ Guess a possible reason why water has a much greater dielectric constant $(=80)$ than say, mica $(=6)$