1. Electric Charges and Fields
hard

$R$ ત્રિજ્યા ધરાવતો અનંત ધન નળાકારમાં અચળ વિજભાર કદ ઘનતા $\rho$ છે. તેના અંદર $R/2$ ત્રિજ્યા ધરાવતી ગોળીય બખોલ છે. જેનું કેન્દ્ર અક્ષ પર છે. નળાકારની અક્ષથી $2R$ અંતરે આવેલ $P$ બિંદુએ વિદ્યુતક્ષેત્ર $\frac{{23\rho R}}{{16K{\varepsilon _0}}}$ હોય તો $K$ નું મૂલ્ય કેટલું હશે?

A

$6$

B

$5$

C

$7$

D

$4$

Solution

We suppose that the cavity is filled up by a positive as well as negative volume charge of $\rho .$ So the electric field now produced at $P$ is the superposition of two electric fields.

$(i)$ The electric field created due to the infinitely long solid cylinder is

$E_{1}=\frac{\rho R}{4 \varepsilon_{0}}$ directed towards the $+Y$ direction

$(ii)$ The electric field created due to the spherical negative charge density

$\mathrm{E}_{2}=\frac{\rho \mathrm{R}}{96 \varepsilon_{0}}$ directed towards the $-Y$ direction.

$\therefore $ The net electric field is

$\mathrm{E}=\mathrm{E}_{1}-\mathrm{E}_{2}=\frac{1}{6}\left[\frac{23 \rho \mathrm{R}}{16 \varepsilon_{0}}\right]$

Standard 12
Physics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.