Download App

Electric Field and Potential — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectric Field and Potential3 Marks
Question
Suppose an attractive nuclear force acts between two protons which may be written as $\text{F}=\text{Ce}^{-\text{kr}}/\text{r}^2.$
  1. Write down the dimensional formulae and appropriate SI units of C and k.
  2. Suppose that k = 1 fermi$^{-1}$ and that the repulsive electric force between the protons is just balanced by the attractive nuclear force when the separation is 5 fermi. Find the value of C.
✓

Answer

Expression of electrical force $\text{F}=\text{C}\times\text{e}^{\frac{-\text{kr}}{\text{r}^2}}$
Since $e^{-kr}$ is a pure number. So, dimensional formulae of $\text{F}=\frac{\text{dimensional formulae of C}}{\text{dimensional formulae of r}^2}$
Or, $\big[\text{MLT}^{-2}\big]\big[\text{L}^2\big]=$ dimensional formulae of $\text{C}=\big[\text{ML}^3\text{T}^{-2}\big]$
Unit of C = unit of force $\times$ unit of $r^2 =$ Newton$ \times m^2 =$ Newton$-m^2$​​​​​​​
Since -kr is a number hence dimensional formulae of
$\text{k}=\frac{1}{\text{dim entional formulae of r}}=\big[\text{L}^{-1}\big]$ Unit of $k = m^{-1}​​​​​​​$​​​​​​​

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

Physics STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A free atom of iron emits $\text{K}_\alpha$ X-rays of energy 6.4keV. Calculate the recoil kinetic energy of the atom. Mass of an iron atom $= 9.3 \times 10^-^{26}kg.$
→
Two charged particles, having equal charges of $2.0 \times 10^{-5}C$ each, are brought from infinity to within a separation of 10cm. Find the increase in the electric potential energy during the process.
→
One end of a spring of natural length h and spring constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h (figure). Initially, the spring makes an angle of 37° with the vertical when the system is released from rest. Find the speed of the ring when the spring becomes vertical.
→
A capacitor of capacitance $100\mu\text{F}$ is connected to a battery of 20 volts for a long time and then disconnected from it. It is now connected across a long solenoid having 4000 turns per metre. It is found that the potential difference across the capacitor drops to 90% of its maximum value in 2.0 seconds. Estimate the average magnetic field produced at the centre of the solenofd during this period.
→
Can we perform Young's double slit experiment with sound waves? To get a reasonable "fringe pattern", what should be the order of separation between the slits? How can the bright fringes and the dark fringes be detected in this case?
→
A block of mass 100g is moved with a speed of 5.0m/s at the highest point in a closed circular tube of radius 10cm kept in a vertical plane. The cross-section of the tube is such that the block just fits in it. The block makes several oscillations inside the tube and finally stops at the lowest point. Find the work done by the tube on the block during the process.
→
Two small balls A and B, each of mass m, are joined rigidly by a light horizontal rod of length L. The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. The system is rotated with an angular speed w about the axis. A particle P of mass m kept at rest sticks to the ball A as the ball collides with it. Find the new angular speed of the rod.
→
An electric field of $20NC^{-1}$ exists along the x-axis in space. Calculate the potential difference $V_B - V_A$ where the points A and B are given by,
  1. $A = (0, 0); B = (4m, 2m)$
  2. $A = (4m, 2m); B = (6m, 5m)$
  3. $A = (0, 0); B = (6m, 5m)$
Do you find any relation between the answers of parts (a), (b) and (c)?
→
An $\alpha-$ particle collides with nucleus after passing through the potential $V$ volt. Prove that distance of closest approach of particle of atomic number $Z$ to the nucleus will be $14.4( Z / V ) \ \mathring A $.
$($Given that : $1 / 4 \pi \varepsilon_0=9.0 \times 10^9$ Newton $-$ meter $^2 /$ Coulomb $^2$ and $e=1.6 \times 10^{-19}$ Coulomb$)$
→
A uniform chain of mass m and length l overhangs a table with its two third part on the table. Find the work to be done by a person to put the hanging part back on the table.
→