11.2-Electric Potential and Potential Difference

11.2-Electric Potential and Potential Difference Important Formulae

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Grade 10 → Science → Electricity → 11.2-Electric Potential and Potential Difference

Electric potential and potential difference are fundamental concepts in electricity that help us understand how electric charges interact within electric fields. In this section, we will define these terms, explore their significance, and discuss their applications.

Definition of Electric Potential

Electric potential (V) at a point in an electric field is defined as the amount of work done in bringing a unit positive charge from infinity to that point without any acceleration. It is measured in volts (V).

The formula for electric potential is given by:

V = W/Q

where W is the work done in joules and Q is the charge in coulombs.

Significance of Electric Potential

Electric potential provides a measure of the energy per unit charge at a specific location in an electric field. It helps in predicting the behavior of charged particles within the field and is crucial for understanding electric circuits.

Definition of Potential Difference

Potential difference (ΔV) between two points in an electric field is defined as the difference in electric potential between those points. It indicates the work done to move a unit charge from one point to another. The formula for potential difference is:

ΔV = V1 - V2

where V1 and V2 are the electric potentials at points 1 and 2, respectively.

Measurement of Electric Potential and Potential Difference

Electric potential and potential difference are measured using a voltmeter, which is connected in parallel across the points where the potential difference is to be measured. Proper connections are essential for accurate readings.

Relation between Electric Potential and Electric Field

The electric potential is related to the electric field (E) by the formula:

ΔV = - ∫ E · dl

This equation shows that the potential difference between two points is equal to the negative integral of the electric field along the path between those points. It indicates that electric fields point in the direction of decreasing potential.

Units of Electric Potential and Potential Difference

The SI unit of electric potential and potential difference is the volt (V). One volt is defined as the potential difference that will move one joule of energy per coulomb of charge.

Applications of Electric Potential and Potential Difference
  • Electrical Circuits: Understanding potential difference is crucial for analyzing and designing electrical circuits, ensuring devices operate safely and efficiently.
  • Power Supply: The potential difference provided by power sources like batteries and generators determines the energy available to run electrical devices.
  • Electrostatics: Concepts of electric potential are essential in electrostatics, affecting how charges interact in various applications.
Factors Affecting Electric Potential

Electric potential is influenced by the following factors:

  • Distance from Charge: The electric potential decreases with an increase in distance from a charge.
  • Magnitude of Charge: Greater charges produce higher electric potentials.
Practical Examples

Understanding electric potential and potential difference is essential for real-world applications:

  • In electronic devices, potential difference dictates the flow of current, enabling their operation.
  • In electrical engineering, potential difference is critical for designing circuits that safely distribute power.


Electric field around a large and a small conducting sphere at opposite electric potential. The shape of the field lines is computed exactly, using the method of image charges with an infinite series of charges inside the two spheres. Field lines are always orthogonal to the surface of each sphere. In reality, the field is created by a continuous charge distribution at the surface of each sphere, indicated by small plus and minus signs. The electric potential is depicted as background color with yellow at 0V.
Geek3, CC BY-SA 4.0, via Wikimedia Commons

11.2-इलेक्ट्रिक पोटेंशियल और पोटेंशियल अंतर

इलेक्ट्रिक पोटेंशियल (Electric Potential) और पोटेंशियल अंतर (Potential Difference) के विचार महत्वपूर्ण हैं क्योंकि ये विद्युत क्षेत्र की ऊर्जा स्थिति को समझाने में मदद करते हैं। जब किसी चार्ज को विद्युत क्षेत्र में रखा जाता है, तो वह ऊर्जा रखता है, जिसे पोटेंशियल ऊर्जा कहते हैं।

इलेक्ट्रिक पोटेंशियल (Electric Potential): किसी बिंदु पर इलेक्ट्रिक पोटेंशियल उस बिंदु पर 1 कूलम्ब चार्ज को लाने के लिए आवश्यक काम की मात्रा होती है, यदि वह चार्ज एक शून्य पोटेंशियल बिंदु से उस स्थान तक लाया जाए। इसे V से व्यक्त किया जाता है और इसकी मात्रक वोल्ट (V) होती है।

सूत्र:
इलेक्ट्रिक पोटेंशियल, $V = \dfrac{W}{Q}$
जहाँ,
$V$ = पोटेंशियल (वोल्ट में),
$W$ = कार्य (जूल में),
$Q$ = चार्ज (कूलम्ब में)

पोटेंशियल अंतर (Potential Difference): किसी दो बिंदुओं के बीच इलेक्ट्रिक पोटेंशियल अंतर उस कार्य की मात्रा होती है, जो 1 कूलम्ब चार्ज को एक बिंदु से दूसरे बिंदु तक ले जाने के लिए करना पड़ता है। इसे ΔV से व्यक्त किया जाता है और इसकी मात्रक भी वोल्ट (V) होती है।

सूत्र:
पोटेंशियल अंतर, $\Delta V = V_B - V_A$
जहाँ,
$V_A$ और $V_B$ क्रमशः बिंदु A और B पर पोटेंशियल हैं।

यदि किसी बिंदु पर पोटेंशियल अधिक है, तो वहां से चार्ज को उस बिंदु पर लाने के लिए कार्य किया जाता है। अगर पोटेंशियल अंतर अधिक है, तो अधिक कार्य करना पड़ता है।

एक और महत्वपूर्ण अवधारणा है: इलेक्ट्रिक पोटेंशियल हमेशा संदर्भ बिंदु से मापा जाता है। आमतौर पर इसे 'अनंत' (infinity) से मापा जाता है, जहाँ पोटेंशियल को शून्य माना जाता है।

बिजली के उपकरणों में पोटेंशियल अंतर: विद्युत ऊर्जा का प्रवाह पोटेंशियल अंतर की वजह से होता है। उदाहरण के लिए, बैटरियों में पोटेंशियल अंतर होता है, जिससे चार्ज को एक बिंदु से दूसरे बिंदु तक भेजा जाता है, जिससे विद्युत प्रवाह (current) उत्पन्न होता है।

पोटेंशियल और विद्युत क्षेत्र (Electric Field): इलेक्ट्रिक पोटेंशियल और विद्युत क्षेत्र के बीच एक महत्वपूर्ण संबंध होता है। यदि किसी बिंदु पर विद्युत क्षेत्र है, तो पोटेंशियल अंतर भी होगा। विद्युत क्षेत्र का पोटेंशियल अंतर के साथ एक अन्य संबंध है:

सूत्र:
$E = -\dfrac{dV}{dx}$
जहाँ,
$E$ = विद्युत क्षेत्र (N/C में),
$dV$ = पोटेंशियल का परिवर्तन,
$dx$ = स्थान का परिवर्तन

यह सूत्र यह बताता है कि यदि पोटेंशियल में परिवर्तन है, तो विद्युत क्षेत्र उस परिवर्तन के विपरीत दिशा में होगा।

Name a device that helps to maintain a potential difference across a conductor.

Solution:

Name a device that helps to maintain a potential difference across a conductor
A device that helps to maintain a potential difference across a conductor is a cell or a battery. A cell is a single electrochemical unit that provides energy to move charges through a circuit, while a battery is a collection of cells connected in series or parallel. The cell or battery creates a difference in electric potential (voltage) between its terminals, allowing electric current to flow through the conductor when connected to an external circuit. This potential difference is essential for maintaining the flow of electrons in the conductor.

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What is meant by saying that the potential difference between two points is 1 V?

Solution:

What is meant by saying that the potential difference between two points is 1 V?
When we say that the potential difference between two points is 1 volt (1 V), it means that 1 joule of work is done to move 1 coulomb of electric charge between those two points. In other words, the energy required to move 1 coulomb of charge across the two points is equal to 1 joule. The formula to express this relationship is: 1 V = 1 J / 1 C This indicates that the potential difference is a measure of the energy transferred per unit charge in an electric circuit.

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How much energy is given to each coulomb of charge passing through a 6 V battery?

Solution:

How much energy is given to each coulomb of charge passing through a 6 V battery?
The energy given to each coulomb of charge passing through a battery can be calculated using the formula: Energy (E) = Voltage (V) × Charge (Q) Here, the voltage (V) is 6 volts, and the charge (Q) is 1 coulomb (since we are calculating for each coulomb of charge). Substituting the values: E = 6 V × 1 C = 6 joules Therefore, 6 joules of energy is given to each coulomb of charge passing through the 6 V battery.

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