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 $(=6)$?
$(a)$ 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 $(=6)$?
(A) No,the force is not exactly given by $Q_{1} Q_{2} / 4 \pi \varepsilon_{0} r^{2}$ because the charge distribution on the spheres becomes non-uniform due to induction when they are brought close to each other.
$(b)$ No,Gauss's law would not be true. Gauss's law is a direct consequence of the inverse-square law ($1/r^{2}$ dependence).
$(c)$ Not necessarily. $A$ test charge will travel along the field line only if the field line is a straight line. If the field line is curved,the force (and acceleration) is tangent to the curve,but the velocity may not be.
$(d)$ The work done is zero in both cases. The electrostatic force is a conservative force,and the work done in a closed path is always zero.
$(e)$ No,the electric potential is continuous across the surface of a charged conductor. Only the electric field is discontinuous.
$(f)$ The capacitance of a single conductor is defined as the capacitance of a system where the second conductor is assumed to be at infinity.
$(g)$ Water molecules have a permanent electric dipole moment,which allows them to align with an external electric field,leading to a much higher dielectric constant compared to non-polar materials like mica.
$(b)$ No,Gauss's law would not be true. Gauss's law is a direct consequence of the inverse-square law ($1/r^{2}$ dependence).
$(c)$ Not necessarily. $A$ test charge will travel along the field line only if the field line is a straight line. If the field line is curved,the force (and acceleration) is tangent to the curve,but the velocity may not be.
$(d)$ The work done is zero in both cases. The electrostatic force is a conservative force,and the work done in a closed path is always zero.
$(e)$ No,the electric potential is continuous across the surface of a charged conductor. Only the electric field is discontinuous.
$(f)$ The capacitance of a single conductor is defined as the capacitance of a system where the second conductor is assumed to be at infinity.
$(g)$ Water molecules have a permanent electric dipole moment,which allows them to align with an external electric field,leading to a much higher dielectric constant compared to non-polar materials like mica.
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$(A)$ For $\beta = \frac{1}{4}$ and $z_0 = \frac{25}{7}R$,the particle reaches the origin.
$(B)$ For $\beta = \frac{1}{4}$ and $z_0 = \frac{3}{7}R$,the particle reaches the origin.
$(C)$ For $\beta = \frac{1}{4}$ and $z_0 = \frac{R}{\sqrt{3}}$,the particle returns back to $z=z_0$.
$(D)$ For $\beta > 1$ and $z_0 > 0$,the particle always reaches the origin.
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