Download App

Electric Charges and Fields — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields3 Marks
Question
Using Gauss’s theorem, show mathematically that for any point outside the shell, the field due to a uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre. Why do you expect the electric field inside the shell to be zero according to this theorem?
✓

Answer

$\phi =\oint\limits_{s}\overrightarrow{\text{E}}.\overrightarrow{\text{d}}\text{s} = \frac{\text{q}}{\varepsilon_{\circ}}$

Derivation: $\text{E}\times4\pi\text{r}^{2} =\frac{\sigma}{\varepsilon_{\circ}}4\pi\text{R}^{2}$

$\therefore \text{E} = \frac{\sigma\text{R}^{2}}{\varepsilon_{\circ}\text{r}^{2}}$

where $\text{q} = 4\pi\text{R}^{2}\sigma$ is the total charge on the spherical shell. Electrostatic field is zero, since total charge inside the shell is zero or charge reside on the surface of the shell.

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 "3 Marks Question" 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

An electric dipole with dipole moment 4 × 10-9 Cm is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 104 NC-1. Calculate the magnitude of the torque acting on the dipole.
→
What is reverse bias? Explain the change occuring in the junction under the effect of reverse bias.
→
Consider a sphere of radius R with charge density distributed as

$\rho\text{(r)}=\text{kr for r}\leq\text{R}$

$=0\text{ for f}>\text{R}.$

Find the electric field at all points r.

→
Three particles, each of mass 200g, are kept at the corners of an equilateral triangle of side 10cm. Find the moment of inertia of the system about an axis:
  1. Joining two of the particles.
  2. Passing through one of the particles and perpendicular to the plane of the particles.
→
An ideal diode should pass a current freely in one direction and should stop it completely in the opposite direction. Which is closer to ideal-vacuum diode or a p-n junction diode?
→
How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.
→
A source of ac voltage v = v0 $\sin\omega t$, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
→
The count rate from a radioactive sample falls from 4.0 × 106 per second to 1.0 × 106 per second in 20 hours. What will be the count rate 100 hours after the beginning?
→

A parallel plate capacitor, each with plate area A and separation d, is charged to a potential difference V. The battery used to charge it is then disconnected. A dielectric slab of thickness d and dielectric constant K is now placed between the plates. What change, if any, will take place in.

  1.  Charge on the plates.
  2. Electric field intensity between the plates.
  3. Capacitance of the capacitor.
→
A 0’5 m long metal rod PQ completes the circuit as shown in the figure. The area of the circuit is perpendicular to the magnetic field of flux density 0-15 T. If the resistance of the total circuit is 3Ω, calcularod in the direction as indicated with a constant speed ofte the force needed to move the rod in the direction as indicated with a constant speed of 2ms−1.

→