10 Questions
What is the expression for the potential at the common center of two concentric shells with surface charge densities $oldsymbol{rac{Q}{4 ext{π}(a+b)^2}}$?
$rac{Q}{4 ext{π}ε_0(a + b)}$
What is the mathematical expression to calculate the electrostatic potential at the origin due to an infinite array of point charges with charge $q$ and distance $x=1,2,4,8,...$?
$rac{q}{4 ext{π}ε_0}$
In the context of electrostatics, what does the expression $oldsymbol{rac{Q}{4 ext{π}(a+b)^2}}$ represent?
Potential at the common center of two concentric shells
In the given system, what condition must be satisfied for the resultant force on charge q to be zero?
The charges q and Q must be of opposite nature.
In Illustration 5, why does the force on the point charge -q at the center of the hexagon become zero if a sixth charge +q is added at the vacant vertex?
The forces due to the six charges balance due to symmetry.
In Illustration 6, what happens to the time period of a charge q when it is slightly displaced from its midpoint position along the line joining two charges of magnitude Q?
The time period increases.
If the separation between two point charges decreases, what happens to the electric potential energy of the system?
Increases
In Illustration 21.Q, if the electric potential energy of the given system is positive, what can be concluded about the relationship between 2Q and 3q?
2Q > 3q
In Illustration 22, if the two nearest charges are mutually interchanged and the potential energy becomes U2, what will be the relationship between U1 and U2?
U1 < U2
Considering Illustration 23, if four charges q each are placed at the four corners of a square of side a, what is the potential energy of one of the charges at corner A?
$\frac{q}{16\pi\varepsilon_0 a}$
Deduce an expression for the electric potential at the common center of two concentric shells with equal surface charge densities. Calculate the total charge given to the shells and derive the equation for the potential at their common center.
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