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Question

(D) The system consists of two parallel disks with surface charge densities $\sigma$ and $-\sigma$,forming an electric dipole.The total charge on each

Vedclass · Accepted Answer

$\frac{{\sigma {R^2}l}}{{2{\varepsilon _0}{r^3}}}$

Vedclass · Answer

(D) The system consists of two parallel disks with surface charge densities $\sigma$ and $-\sigma$,forming an electric dipole.The total charge on each disk is $Q = \sigma A = \sigma \pi R^2$.The dipole moment $p$ of this system is given by $p = Ql = \sigma \pi R^2 l$.For a point $P$ at a large distance $r$ along the axis of the dipole,the electric field $E$ is given by the formula for the axial field of a dipole:$E = \frac{1}{4\pi \varepsilon_0} \cdot \frac{2p}{r^3}$.Substituting the value of $p$:$E = \frac{1}{4\pi \varepsilon_0} \cdot \frac{2(\sigma \pi R^2 l)}{r^3}$.Simplifying the expression:$E = \frac{2 \sigma \pi R^2 l}{4 \pi \varepsilon_0 r^3} = \frac{\sigma R^2 l}{2 \varepsilon_0 r^3}$.

Two parallel disks each having radius $R$ are separated by a distance $l$. The surface charge densities are $\sigma$ and $-\sigma$. The electric field at point $P$,a large distance $r$ along the axis of the disks is:

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