A uniformly charged solid sphere of radius R | vedclass

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Question

We know, $\mathrm{V}_{0}=\frac{\mathrm{Kq}}{\mathrm{R}}=\mathrm{V\,surface}$

Now, $\mathrm{V}_{\mathrm{i}}=\frac{\mathrm{Kq}}{2 \mathrm{R}^{3}}\lef

Vedclass · Accepted Answer

$2R < R_4$

Vedclass · Answer

We know, $\mathrm{V}_{0}=\frac{\mathrm{Kq}}{\mathrm{R}}=\mathrm{V\,surface}$

Now, $\mathrm{V}_{\mathrm{i}}=\frac{\mathrm{Kq}}{2 \mathrm{R}^{3}}\left(3 \mathrm{R}^{2}-\mathrm{r}^{2}\right) \quad[\mathrm{For}\, \mathrm{r}<\mathrm{R}]$

At the centre of sphare $r=0 .$

Here $\mathrm{V}=\frac{3}{2} \mathrm{V}_{0}$

Now, $\frac{5}{4} \frac{\mathrm{Kq}}{\mathrm{R}}=\frac{\mathrm{Kq}}{2 \mathrm{R}^{3}}\left(3 \mathrm{R}^{2}-\mathrm{r}^{2}\right)$

$\mathrm{R}_{2}=\frac{\mathrm{R}}{\sqrt{2}}$

$\frac{3}{4} \frac{\mathrm{Kq}}{\mathrm{R}}=\frac{\mathrm{Kq}}{\mathrm{R}^{3}}$

$\frac{1}{4} \frac{\mathrm{Kq}}{\mathrm{R}}=\frac{\mathrm{Kq}}{\mathrm{R}_{4}}$

$\mathrm{R}_{4}=4 \mathrm{R}$

Also, $\mathrm{R}_{1}=0$ and $\mathrm{R}_{2}<\left(\mathrm{R}_{4}-\mathrm{R}_{3}\right)$

Similar Questions

Two charges $2 \;\mu\, C$ and $-2\; \mu \,C$ are placed at points $A$ and $B\;\; 6 \;cm$ apart.

$(a)$ Identify an equipotential surface of the system.

$(b)$ What is the direction of the electric field at every point on this surface?

What is an equipotential surface ? Draw an equipotential surfaces for a

$(1)$ single point charge

$(2)$ charge $+ \mathrm{q}$ and $- \mathrm{q}$ at few distance (dipole)

$(3)$ two $+ \mathrm{q}$ charges at few distance

$(4)$ uniform electric field.

Draw an equipotential surface of two identical positive charges for small distance.

Assertion : Two equipotential surfaces cannot cut each other.

Reason : Two equipotential surfaces are parallel to each other.

Assertion $(A):$ A spherical equipotential surface is not possible for a point charge.

Reason $(R):$ A spherical equipotential surface is possible inside a spherical capacitor.

Similar Questions

Two charges $2 \;\mu\, C$ and $-2\; \mu \,C$ are placed at points $A$ and $B\;\; 6 \;cm$ apart. $(a)$ Identify an equipotential surface of the system. $(b)$ What is the direction of the electric field at every point on this surface?

What is an equipotential surface ? Draw an equipotential surfaces for a $(1)$ single point charge $(2)$ charge $+ \mathrm{q}$ and $- \mathrm{q}$ at few distance (dipole) $(3)$ two $+ \mathrm{q}$ charges at few distance $(4)$ uniform electric field.

Draw an equipotential surface of two identical positive charges for small distance.

Assertion : Two equipotential surfaces cannot cut each other. Reason : Two equipotential surfaces are parallel to each other.

Assertion $(A):$ A spherical equipotential surface is not possible for a point charge. Reason $(R):$ A spherical equipotential surface is possible inside a spherical capacitor.

Two charges $2 \;\mu\, C$ and $-2\; \mu \,C$ are placed at points $A$ and $B\;\; 6 \;cm$ apart.

$(a)$ Identify an equipotential surface of the system.

$(b)$ What is the direction of the electric field at every point on this surface?

What is an equipotential surface ? Draw an equipotential surfaces for a

$(1)$ single point charge

$(2)$ charge $+ \mathrm{q}$ and $- \mathrm{q}$ at few distance (dipole)

$(3)$ two $+ \mathrm{q}$ charges at few distance

$(4)$ uniform electric field.

Assertion : Two equipotential surfaces cannot cut each other.

Reason : Two equipotential surfaces are parallel to each other.

Assertion $(A):$ A spherical equipotential surface is not possible for a point charge.

Reason $(R):$ A spherical equipotential surface is possible inside a spherical capacitor.