Home/Class 12/Physics/

Question and Answer

Calculate the potential at a point  \(P\)  due to a charge of  \(4\times 10^{-7}C\)  located  \(9\text{ cm}\)  away. Hence obtain the work done in bringing a charge of  \(2\times 10^{-9}C\)  from infinity to the point  \(P\) . Does the answer depend on the path along which the charge is brought?
loading
settings
Speed
00:00
01:52
fullscreen
Calculate the potential at a point  \(P\)  due to a charge of  \(4\times 10^{-7}C\)  located  \(9\text{ cm}\)  away. Hence obtain the work done in bringing a charge of  \(2\times 10^{-9}C\)  from infinity to the point  \(P\) . Does the answer depend on the path along which the charge is brought?

Answer

See analysis below
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
To Keep Reading This Answer, Download the App
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play

Solution

Given :
Solution for Calculate the potential at a point  P  due to a charge of  4times 10^{-7}C  located  9text{ cm}  away. Hence obtain the work done in bringing a charge of  2times 10^{-9}C  from infinity to the point  P . Does the answer depend on the path along which the charge is brought?
 \(Q=4\times 10^{-7}C,r=0.09\;m\) 
For source charge, Potential at  \(P\)  due to  \(Q\)  charge,
  \(V_P=\left(\frac 1{4\pi \varepsilon _0}\right)\left(\frac Q r\right)\)
 \(=\frac{\left(9\times 10^9\right)\left(4\times 10^{-7}\right)}{0.09}\)
 \(=4\times 10^4\;V\)
Given data,
Test charge, \(q=2\times 10^{-9}C\)
Potential at point  \(P=\)   \(4\times 10^4\;V\)
Potential at a point (test charge) is the amount of work done to bring unit charge from infinity to that point.
  \(W_{{\infty}P}=qV_p\)
 \(=2\times 10^{-9}\times 4\times 10^4\)
 \(=8\times 10^{-5}\;J\)
No, this work done does not depend on the path followed. The reason is that this work is against electrostatic force which is a conservative force.
To Keep Reading This Solution, Download the APP
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
To Keep Reading This Solution, Download the APP
4.6
star pngstar pngstar pngstar pngstar png
Review from Google Play
Correct16
Incorrect0
Watch More Related Solutions
A satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 km above the earth’s surface. Find its time period. Consider mass of the earth = \( 6\times {10}^{24}\) kg
Two charges \(3\times 10^{-8}\;\text C\) and \(-2\times 10^{-8}\;\text C\)  are located \(15\;\text{cm}\)  apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
Figures \((a)\) and \((b)\) show the field lines of a positive and negative point charge respectively.

Give the signs of the potential difference  \(V_{\text P}-V_{\text Q}\) and \(V_{\text B}-V_{\text A} .\)
A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second are heard. The beat frequency reduces if the tension in the string is slightly increased. The original frequency of vibration of the string is
(a) 506 Hz
(b) 512 Hz
(c) 518 Hz
(d) 524 Hz.
Figures \((a)\) and \((b)\) show the field lines of a positive and negative point charge respectively.

Give the sign of the potential energy difference of a small negative charge between the points \(Q\)  and \(P:A\)  and \(B\)
A person can hear sound waves in the frequency range \( 20\;Hz\) to \( 20\;kHz\). Find the minimum and maximum wavelengths of sound that is audible to the person. The speed of sound is \( 360\;m/s.\)
Figures \((a)\) and \((b)\) show the field lines of a positive and negative point charge respectively.

Give the sign of the work done by the field in moving a small positive charge from \(Q\)  to \(P\) .
At Deoprayag (Garwal, UP) river Alaknande mixes with the river Bhagirathi and becomes river Ganga. Suppose Alaknanda has a width of \(12 \;m\), Bhagirathi has a width of \(8\;m\) and Ganga has a width of \(16 \;m\). Assume that the depth of water is same in the three rivers, let the average speed of water in Alaknanda be \( 20\;km {h}^{-1}\) and in Bhagirathi be \( 16\;km {h}^{-1}.\) Find the average speed of water in the river Ganga.
Determine the electrostatic potential energy of a system consisting of two charges \(7\;\mu C\)  and \(-2\;\mu C\) \( (\)and with no external field\() \)placed \((0.0)\)  respectively. at \(\left(-9\;\text{cm},0,0\right)\)  and \((9\;\text{cm} ,0,0) \) respectively.
A system consisting of two charges  \(7\;\mu C\)  and  \(-2\;\mu C\)  (and with no external field) placed  \((0.0)\)  respectively. at  \(\left(-9\; \text{cm},0,0\right)\)  and \((9\; \text{cm},0,0)\) respectively. How much work is required to separate the two charges infinitely away from each other?

Load More