Potential difference (ΔV) between two points A and B separated

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Case study question of Physics – Electrostatic potential and capacitance 

Case study 4:- Potential difference (ΔV) between two points A and B separated by a distance x in a uniform electric field E is given by ΔV = -Ex, where, x is measured parallel to the field lines. If a charge q_0 moves from P to Q, the changes in potential energy (ΔU) is given as ΔU = q_0\delta V. A proton is released from rest in uniform electric field of magnitude 4.0\times 10^8 Vm^{-1} directly along the positive X-axis. The proton undergoes a displacement of 0.25 m in the direction of E.

Mass of a proton = 1.66 \times 10^{-27} kg and charge of proton =1.6 \times 10^{-19} C

Read the given passage carefully and give the answer the following questions:

Q 1:- What will be the change in electric potential of the proton between the points A and B ?

Q 2:- What will the change in electric potential energy of the proton for displacement from A to B ?

Q 3:- Calculate the mutual electrostatic potential energy between two protons which are at a distance of 9\times 10^{-15} m, in {}_{92}U^{235} nucleus.

Q 4:- If a system consists of two charges 4 μC and -3 μC with no external field placed at (-5 cm, 0, 0) and (5 cm, 0, 0) respectively. find the amount of work required to separate the two charges infinitely away from each other.

Q 5:- As the proton moves from P to Q, then what will happen ?

Answer :- 1.  ΔV = -EΔX

= -(4\times 10^8)\times 0.25 = -10^8 V

2.  As ΔU = qΔV

= 1.6\times 10^{-19} \times(-1.0 \times 10^8)

= -1.6 \times 10^{-11} J

3. Potential energy. U = \dfrac{1}{4\pi \epsilon _0}\dfrac{q_1q_2}{r}

=\dfrac{9\times 10^9 \times 1.6 \times 10^{-19}\times 1.6\times 10^{-19}}{9\times 10^{-15}}

= 2.56 \times 10^{-14} J

4. U = \dfrac{1}{4\pi \epsilon _0}\dfrac{q_1q_2}{r}

= \dfrac{9\times 10^9 \times 4 \times 10^{-6} \times (-3) \times 10^{-6}}{0.1}

= -11 J

5. As proton moves in the direction of the electric field or from P to Q then its potential energy decreases

Case study 1:- The potential at any observation point P of a static electric field is defined as the work done by the external agent (or negative of work done by electrostatic field) in slowly bringing a unit positive point charge from infinity to the observation point. Figure shows the potential variation along the line of charges. Two point charges Q_1 and Q_2 lie along a line at a distance from each other.

The potential at any observation point P of a static electric

Read the given passage carefully and give the answer of the following questions:

Q 1. At which of the points 1, 2 and 3 is the electric field zero ?

(a) 1                 (b) 2

(c) 3                  (d) Both a. and b.

Solution:- See full solution

Case study 2:- This energy possessed by a system of charges by virtue of their positions. When two like charges lie infinite distance apart, their potential energy is zero because no work has to be done in moving one charge at infinite distance from the other. In carrying a charge q from point A to point B, work done W = q(V_A - V_B). this may appear as change in KE/PE of the charge. The potential energy of two charges q_1 and q_2 at a distance r in air is \dfrac{q_1q_2}{4\pi \epsilon _0 r}. It is measured in joule. It may be positive, negative or zero depending on the signs of q_1 and q_2.

Read the given passage carefully and give the answer of the following questions:

Solution:- See full solution

Case study 3:- Animals emit low frequency electric fields due to a process known as osmoregulation. This process allows the concentration of ions (charged atoms or molecules) to flow between the inside of our bodies and the outside. In order for our cells to stay intact, the flow of ions needs to be balanced. But balanced doesn’t necessarily mean equal. The concentration of ions within a shrimp’s body is much lower than that of the sea water it swims in. Their voltage or potential sifference generated between the two concentrations across ‘leaky’ surfaces, can then be measured.

Read the given passage carefully and give the answer of the following questions:

Solution:- See full solution

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