A particle of charge $Q$ and mass $M$ moves in a circular path of radius $R$ in a uniform magnetic field of magnitude $B$. The same particle now moves with the same speed in a circular path of same radius $R$ in the space between the cylindrical electrodes of the cylindrical capacitor. The radius of the inner electrode is $R/2$ while that of the outer electrode is $ 3R/2.$ Then the potential difference between the capacitor electrodes must be
A particle of charge $Q$ and mass $M$ moves in a circular path of radius $R$ in a uniform magnetic field of magnitude $B$. The same particle now moves with the same speed in a circular path of same radius $R$ in the space between the cylindrical electrodes of the cylindrical capacitor. The radius of the inner electrode is $R/2$ while that of the outer electrode is $ 3R/2.$ Then the potential difference between the capacitor electrodes must be
- A
$QBR\,\,(ln3)/ M$
- B
$QB^2R^2\,\, (ln3)/ 2M$
- C
$QB^2R ^2 \,\,(ln3)/ M$
- D
None
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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?
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$(c)$ $A$ 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 $(=6)$