Download App

Electric Charges and Fields — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields2 Marks
Question
The electric potential inside a charged spherical ball is given by $\phi=a r^2+b$. Where $r$ is the distance from the centre, $a$ and $b$ are constants. Calculate the charge density inside the ball.
✓

Answer

$\phi=a r^2+b$
$E =\frac{d \phi}{d t}=-2 a r$
$\oint \overrightarrow{ E } \cdot d \overrightarrow{ S }=\frac{q}{\in_0}$
$-2 a r \cdot 4 \pi r^2=\frac{q}{\in_0}$
$a=-8 \pi \in_0 a r^3$
charge density $\rho=\frac{q}{\frac{4}{3} \pi r^3}=-\frac{8 \pi \in_0 a r^3}{\frac{4}{3} \pi r^3}$
$\rho=-6 a \in_0$ Ans.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Electric Charges and Fields→Electric Charges and Fields — all question types→Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A pivoted aluminium bar falls much more slowly through a small region containing a magnetic field than a similar bar of an insulating material. Explain.
→
Write any three characteristics, a ferromagnetic substance should possess if it is to be used to make a permanent magnet. Give one example of such a material.
→
Can there be a potential difference between two adjacent conductors carrying the same charge?
→
By explaining the (Electric) current density, derive Ohm's law in vector form.
→
Rain is falling vertically. A man running on the road keeps his umbrella tilted but a man standing on the street keeps his umbrella vertical to protect himself from the rain. But both of them keep their umbrella vertical to avoid the vertical sun-rays. Explain.
→
A coil of N turns is wound tightly in the form of a spiral whose internal and external radii $r_1$ are $r_2$ and respectively. Current $I$ is flowing through the coil, then calculate the magnetic field at the center.
→
A circular wire-loop of radius a carries a total charge Q distributed uniformly over its length. A small length dL of the wire is cut off. Find the electric field at the centre due to the remaining wire.
→
The ratio of radii of two nuclei is $1: 2$. Write the ratio of their mass numbers.
→
Discuss sign convention of distances for reflection by spherical mirror and refraction by spherical lens.
→
12J of work has to be done against an existing electric field to take a charge of 0.01C from A to B. How much is the potential difference VB - VA?
→