Two concentric rings- one of radius -a- and the other of radius - b - have the charges -q- and -2-5-3-2 respectively- as shown in the figure- Find the ratio b - a if a charge particle placed on the axis at z - a is in equilibrium- -

Let electric fields produced due to inner and outer rings be E_a and E_b repectively. nbsp; Let the charge on the particle placed at distance z from the cente ...

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Standard XII

Physics

Electric Field Due to a Ring Along the Axis

Two concentri...

Question

Two concentric rings, one of radius ‘a’ and the other of radius ‘b’, have the charges +q, and $- {(\frac{2}{5})}^{\frac{- 3}{2}}$ respectively, as shown in the figure. Find the ratio $\frac{b}{a}$ if a charge particle placed on the axis at z = a is in equilibrium.

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Solution

Let electric fields produced due to inner and outer rings be $E_{a}$ and $E_{b}$ repectively.
Let the charge on the particle placed at distance z from the center of ring be $q_{1}$ .
So, as the particle is in equilibrium at this position
$⟹ q_{1} E_{a} + q_{1} E_{b} = 0$ .........(i)
$⟹ q_{1} \frac{k q a}{(a^{2} + a^{2})^{\frac{3}{2}}} = q_{1} \times \frac{k (\frac{2}{5})^{(} \frac{- 3}{2}) q a}{(a^{2} + b^{2})^{\frac{3}{2}}}$
On further simplifying the above equation we will get
$\frac{b}{a} = 2$

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Two concentric rings, one of radius ‘a’ and the other of radius ‘b’, have the charges +q, and −(25)−32 respectively, as shown in the figure. Find the ratio ba if a charge particle placed on the axis at z = a is in equilibrium.

Two concentric rings, one of radius ‘a’ and the other of radius ‘b’, have the charges +q, and $- {(\frac{2}{5})}^{\frac{- 3}{2}}$ respectively, as shown in the figure. Find the ratio $\frac{b}{a}$ if a charge particle placed on the axis at z = a is in equilibrium.