Consider the following statements regarding Electric Potential:
1. Electric potential is defined as work done in bringing a unit positive charge from infinity to a point.
2. Potential difference between two points is independent of the path taken between them.
3. Electric potential is a vector quantity since it has magnitude and direction.
4. Equipotential surfaces are always perpendicular to electric field lines.
Which of the above statements is/are correct?
Answer & step-by-step solution
The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles. Key relation: E=−∇V; ΔV=−∫E·dl.
Exam focus: Potential is scalar; electric field is vector. Common trap: Do not assign a direction to electric potential.
Statement-wise Verification
- Statement 1 - Correct.
Electric potential is defined as work done in bringing a unit positive charge from infinity to a point.
Potential is scalar; electric field is vector. - Statement 2 - Correct.
Potential difference between two points is independent of the path taken between them.
The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. - Statement 3 - Incorrect.
Electric potential is a vector quantity since it has magnitude and direction.
The correct principle is: Potential is scalar; electric field is vector. - Statement 4 - Correct.
Equipotential surfaces are always perpendicular to electric field lines.
Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.
Core Concept
Electrostatic potential is a scalar. The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.
Formula / Key Relationship
E=−∇V; ΔV=−∫E·dl.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 3. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option C is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1, 4.
Exam Shortcut / Approach
Potential is scalar; electric field is vector.
Common Mistake
Do not assign a direction to electric potential.
Quick Revision
Potential and Equipotential Surfaces is linked with Electric Potential, Electrostatics and Electromagnetic Fields. Potential is scalar; electric field is vector.
विद्युत विभव के संबंध में निम्नलिखित कथनों पर विचार कीजिए:
1. विद्युत विभव अनंत से किसी बिंदु तक इकाई धनात्मक आवेश लाने में किया गया कार्य है।
2. दो बिंदुओं के बीच विभवांतर उनके बीच लिए गए पथ से स्वतंत्र है।
3. विद्युत विभव सदिश राशि है क्योंकि इसमें परिमाण और दिशा होती है।
4. समविभव सतहें हमेशा विद्युत क्षेत्र रेखाओं के लंबवत होती हैं।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
स्थिरविद्युत क्षेत्र संरक्षी होने से विभवांतर पथ-स्वतंत्र है और विद्युत क्षेत्र विभव का ऋणात्मक ग्रेडिएंट है। इसलिए समविभव सतहें क्षेत्र रेखाओं को समकोण पर काटती हैं। मुख्य संबंध: E=−∇V; ΔV=−∫E·dl।
परीक्षा फोकस: विभव अदिश है; विद्युत क्षेत्र सदिश। सामान्य गलती: विभव को दिशा देना।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Electric potential is defined as work done in bringing a unit positive charge from infinity to a point.
Potential is scalar; electric field is vector. - Statement 2 - Correct.
Potential difference between two points is independent of the path taken between them.
The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. - Statement 3 - Incorrect.
Electric potential is a vector quantity since it has magnitude and direction.
The correct principle is: Potential is scalar; electric field is vector. - Statement 4 - Correct.
Equipotential surfaces are always perpendicular to electric field lines.
Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.
Core Concept
Electrostatic potential is a scalar. The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.
Formula / Key Relationship
E=−∇V; ΔV=−∫E·dl.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 3. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option C is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1, 4.
Exam Shortcut / Approach
Potential is scalar; electric field is vector.
Common Mistake
Do not assign a direction to electric potential.
Quick Revision
Potential and Equipotential Surfaces is linked with Electric Potential, Electrostatics and Electromagnetic Fields. Potential is scalar; electric field is vector.
વિદ્યુત સ્થિતિમાન સંબંધિત નીચેના વિધાનો ધ્યાનમાં લો:
1. વિદ્યુત સ્થિતિમાન એટલે અનંતથી કોઈ બિંદુ સુધી એકમ ધન વિદ્યુતભાર લાવવામાં થયેલું કાર્ય.
2. બે બિંદુઓ વચ્ચેનો સ્થિતિમાન તફાવત તેમની વચ્ચે લીધેલા માર્ગથી સ્વતંત્ર છે.
3. વિદ્યુત સ્થિતિમાન સદિશ રાશિ છે કારણ કે તેને માન અને દિશા હોય છે.
4. સમસ્થિતિમાન સપાટીઓ હંમેશા વિદ્યુત ક્ષેત્ર રેખાઓને લંબ હોય છે.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
સ્થિરવિદ્યુત ક્ષેત્ર સંરક્ષી હોવાથી સ્થિતિમાન તફાવત માર્ગ-સ્વતંત્ર છે અને વિદ્યુત ક્ષેત્ર સ્થિતિમાનનો ઋણ ગ્રેડિયન્ટ છે. તેથી સમસ્થિતિમાન સપાટીઓ ક્ષેત્ર રેખાઓને કાટખૂણે છેદે છે. મુખ્ય સંબંધ: E=−∇V; ΔV=−∫E·dl.
પરીક્ષા મુદ્દો: સ્થિતિમાન અદિશ છે; વિદ્યુત ક્ષેત્ર સદિશ. સામાન્ય ભૂલ: સ્થિતિમાનને દિશા આપવી.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Electric potential is defined as work done in bringing a unit positive charge from infinity to a point.
Potential is scalar; electric field is vector. - Statement 2 - Correct.
Potential difference between two points is independent of the path taken between them.
The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. - Statement 3 - Incorrect.
Electric potential is a vector quantity since it has magnitude and direction.
The correct principle is: Potential is scalar; electric field is vector. - Statement 4 - Correct.
Equipotential surfaces are always perpendicular to electric field lines.
Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.
Core Concept
Electrostatic potential is a scalar. The potential difference is path-independent because electrostatic fields are conservative, and electric field is the negative gradient of potential. Equipotential surfaces therefore have no tangential electric-field component and intersect field lines at right angles.
Formula / Key Relationship
E=−∇V; ΔV=−∫E·dl.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 3. Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 2, 4. Option C is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1, 4.
Exam Shortcut / Approach
Potential is scalar; electric field is vector.
Common Mistake
Do not assign a direction to electric potential.
Quick Revision
Potential and Equipotential Surfaces is linked with Electric Potential, Electrostatics and Electromagnetic Fields. Potential is scalar; electric field is vector.
More Electrostatics questions