यह स्थिति विस्थापन शून्य है ।
-9. किसे
अतः कार्य = बल x 0 = 0
ऊज
3 एक बैटरी बल्ब जलाती है। इस प्रक्रम में होने वाले ऊजा
परिवर्तनों का वर्णन कीजिए।
(i) रासायनिक ऊर्जा, विद्युत ऊर्जा में परिवर्तित होती है।
(ii) विद्युत ऊर्जा, ऊष्मा ऊर्जा में परिवर्तित होती है।
(iii) ऊष्मा ऊर्जा प्रकाश ऊर्जा में बदलती है।
A 20 kg द्रव्यमान पर लगने वाला कोई बल वेग को 5 m s'से
2m s1में परिवर्तित कर देता है। बल द्वारा किए गए कार्य का |
परिकलन कीजिए।
द्रव्यमान, m = 20 kg
प्रारम्भिक वेग, 14 = 5ms1
अन्तिम वेग ) =2ms1
.
Answers
Electric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects.
The term "electric potential energy" is used to describe the potential energy in systems with time-variant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with time-invariant electric fields.
Definition
The electric potential energy of a system of point charges is defined as the work required assembling this system of charges by bringing them close together, as in the system from an infinite distance.
The electrostatic potential energy, U, of one point charge q at position r in the presence of an electric field E is defined as the negative of the work W done by the electrostatic force to bring it from the reference position r[note 1] to that position r.[1][2]:§25-1[note 2]
{\displaystyle U_{\mathrm {E} }(\mathbf {r} )=-W_{r_{\rm {ref}}\rightarrow r}=-\int _{{\mathbf {r} }_{\rm {ref}}}^{\mathbf {r} }q\mathbf {E} (\mathbf {r'} )\cdot \mathrm {d} \mathbf {r'} } {\displaystyle U_{\mathrm {E} }(\mathbf {r} )=-W_{r_{\rm {ref}}\rightarrow r}=-\int _{{\mathbf {r} }_{\rm {ref}}}^{\mathbf {r} }q\mathbf {E} (\mathbf {r'} )\cdot \mathrm {d} \mathbf {r'} },
where E is the electrostatic field and dr' is the displacement vector in a curve from the reference position r to the final position r.
The electrostatic potential energy can also be defined from the electric potential as follows:
The electrostatic potential energy, U, of one point charge q at position r in the presence of an electric potential {\displaystyle \scriptstyle \Phi } \scriptstyle \Phi is defined as the product of the charge and the electric potential.
{\displaystyle U_{\mathrm {E} }(\mathbf {r} )=q\Phi (\mathbf {r} )} U_{{\mathrm {E}}}({\mathbf r})=q\Phi ({\mathbf r}),
where {\displaystyle \scriptstyle \Phi } \scriptstyle \Phi is the electric potential generated by the charges, which is a function of position r.
Units
The SI unit of electric potential energy is the joule (named after the English physicist James Prescott Joule). In the CGS system the erg is the unit of energy, being equal to 10−7 J. Also electronvolts may be used, 1 eV = 1.602×10−19 J.
Electrostatic potential energy of one point charge
One point charge q in the presence of another point charge Q
A point charge q in the electric field of another charge Q.
The electrostatic potential energy, U, of one point charge q at position r in the presence of a point charge Q, taking an infinite separation between the charges as the reference position, is:
{\displaystyle U_{E}(r)=k_{e}{\frac {qQ}{r}}} U_{E}(r)=k_{e}{\frac {qQ}{r}},
where {\displaystyle k_{e}={\frac {1}{4\pi \varepsilon _{0}}}} k_{e}={\frac {1}{4\pi \varepsilon _{0}}} is Coulomb's constant, r is the distance between the point charges q & Q, and q & Q are the charges (not the absolute values of the charges—i.e., an electron would have a negative value of charge when placed in the formula). The following outline of proof states the derivation from the definition of electric potential energy and Coulomb's law to this formula.
One point charge q in the presence of n point charges Q
Electrostatic potential energy of q due to Q and Q charge system: {\displaystyle U_{E}=q{\frac {1}{4\pi \varepsilon _{0}}}\left({\frac {Q_{1}}{r_{1}}}+{\frac {Q_{2}}{r_{2}}}\right)} U_{E}=q{\frac {1}{4\pi \varepsilon _{0}}}\left({\frac {Q_{1}}{r_{1}}}+{\frac {Q_{2}}{r_{2}}}\right)
The electrostatic potential energy, U, of one point charge q in the presence of n point charges Q, taking an infinite separation between the charges as the reference position, is:
{\displaystyle U_{E}(r)=k_{e}q\sum _{i=1}^{n}{\frac {Q_{i}}{r_{i}}}} U_{E}(r)=k_{e}q\sum _{{i=1}}^{n}{\frac {Q_{i}}{r_{i}}},
where {\displaystyle k_{e}={\frac {1}{4\pi \varepsilon _{0}}}} k_{e}={\frac {1}{4\pi \varepsilon _{0}}} is Coulomb's constant, r is the distance between the point charges q & Q, and q & Q are the signed values of the charges.
Electrostatic potential energy stored in a system of point charges
The electrostatic potential energy U stored in a system of N charges q, q, ..., q at positions r, r, ..., r respectively, is: