Consider the following statements regarding Conductors in Electrostatics:
1. Electric field inside a perfect conductor under electrostatic conditions is zero due to free charge redistribution.
2. Charges in a conductor reside only on the surface in electrostatic equilibrium.
3. Potential inside a conductor remains constant throughout its volume.
4. Electric field inside a conductor increases with depth due to induced charges.
Which of the above statements is/are correct?
Answer & step-by-step solution
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. The conductor is then an equipotential body and excess free charge resides on its surface. Key relation: Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant.
Exam focus: Zero internal E and constant potential are two views of the same equilibrium condition. Common trap: The field does not increase with depth inside an ideal conductor.
Statement-wise Verification
- Statement 1 - Correct.
Electric field inside a perfect conductor under electrostatic conditions is zero due to free charge redistribution.
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. - Statement 2 - Correct.
Charges in a conductor reside only on the surface in electrostatic equilibrium.
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. - Statement 3 - Correct.
Potential inside a conductor remains constant throughout its volume.
Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant. - Statement 4 - Incorrect.
Electric field inside a conductor increases with depth due to induced charges.
The correct principle is: In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero.
Core Concept
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. The conductor is then an equipotential body and excess free charge resides on its surface. If a nonzero internal field remained, free charge would continue to move, contradicting equilibrium.
Formula / Key Relationship
Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 2. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1.
Exam Shortcut / Approach
Zero internal E and constant potential are two views of the same equilibrium condition.
Common Mistake
The field does not increase with depth inside an ideal conductor.
Quick Revision
Electrostatic Equilibrium in Conductors is linked with Conductors, Electrostatics and Electromagnetic Fields. Zero internal E and constant potential are two views of the same equilibrium condition.
स्थिरविद्युत में चालकों के संबंध में निम्नलिखित कथनों पर विचार कीजिए:
1. स्थिरविद्युत स्थितियों में मुक्त आवेश पुनर्वितरण के कारण पूर्ण चालक के भीतर विद्युत क्षेत्र शून्य होता है।
2. स्थिरविद्युत संतुलन में चालक के आवेश केवल सतह पर रहते हैं।
3. चालक के भीतर विभव पूरे आयतन में स्थिर रहता है।
4. प्रेरित आवेशों के कारण चालक के भीतर विद्युत क्षेत्र गहराई के साथ बढ़ता है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
स्थिरविद्युत संतुलन में चालक के मुक्त आवेश तब तक पुनर्वितरित होते हैं जब तक आंतरिक विद्युत क्षेत्र शून्य न हो। तब चालक समविभव पिंड होता है और अतिरिक्त आवेश सतह पर रहता है। मुख्य संबंध: पूर्ण चालक के भीतर E=0 और V=स्थिर।
सामान्य गलती: आदर्श चालक के भीतर क्षेत्र गहराई के साथ नहीं बढ़ता।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Electric field inside a perfect conductor under electrostatic conditions is zero due to free charge redistribution.
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. - Statement 2 - Correct.
Charges in a conductor reside only on the surface in electrostatic equilibrium.
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. - Statement 3 - Correct.
Potential inside a conductor remains constant throughout its volume.
Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant. - Statement 4 - Incorrect.
Electric field inside a conductor increases with depth due to induced charges.
The correct principle is: In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero.
Core Concept
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. The conductor is then an equipotential body and excess free charge resides on its surface. If a nonzero internal field remained, free charge would continue to move, contradicting equilibrium.
Formula / Key Relationship
Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 2. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1.
Exam Shortcut / Approach
Zero internal E and constant potential are two views of the same equilibrium condition.
Common Mistake
The field does not increase with depth inside an ideal conductor.
Quick Revision
Electrostatic Equilibrium in Conductors is linked with Conductors, Electrostatics and Electromagnetic Fields. Zero internal E and constant potential are two views of the same equilibrium condition.
સ્થિરવિદ્યુતમાં વાહકો સંબંધિત નીચેના વિધાનો ધ્યાનમાં લો:
1. સ્થિરવિદ્યુત સ્થિતિમાં મુક્ત વિદ્યુતભારના પુનઃવિતરણને કારણે સંપૂર્ણ વાહકની અંદર વિદ્યુત ક્ષેત્ર શૂન્ય હોય છે.
2. સ્થિરવિદ્યુત સંતુલનમાં વાહકના વિદ્યુતભાર ફક્ત સપાટી પર રહે છે.
3. વાહકની અંદર સ્થિતિમાન સમગ્ર કદમાં અચળ રહે છે.
4. પ્રેરિત વિદ્યુતભારને કારણે વાહકની અંદર વિદ્યુત ક્ષેત્ર ઊંડાઈ સાથે વધે છે.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
સ્થિરવિદ્યુત સંતુલનમાં વાહકના મુક્ત વિદ્યુતભાર ત્યાં સુધી પુનઃવિતરિત થાય છે જ્યાં સુધી આંતરિક વિદ્યુત ક્ષેત્ર શૂન્ય ન થાય. ત્યારે વાહક સમસ્થિતિમાન પદાર્થ બને છે અને વધારાનો વિદ્યુતભાર સપાટી પર રહે છે. મુખ્ય સંબંધ: સંપૂર્ણ વાહકની અંદર E=0 અને V=અચળ.
સામાન્ય ભૂલ: આદર્શ વાહકની અંદર ક્ષેત્ર ઊંડાઈ સાથે વધતું નથી.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Electric field inside a perfect conductor under electrostatic conditions is zero due to free charge redistribution.
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. - Statement 2 - Correct.
Charges in a conductor reside only on the surface in electrostatic equilibrium.
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. - Statement 3 - Correct.
Potential inside a conductor remains constant throughout its volume.
Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant. - Statement 4 - Incorrect.
Electric field inside a conductor increases with depth due to induced charges.
The correct principle is: In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero.
Core Concept
In electrostatic equilibrium, free charges in a conductor redistribute until the internal electric field is zero. The conductor is then an equipotential body and excess free charge resides on its surface. If a nonzero internal field remained, free charge would continue to move, contradicting equilibrium.
Formula / Key Relationship
Inside a perfect conductor at electrostatic equilibrium: E=0 and V=constant.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 2. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1.
Exam Shortcut / Approach
Zero internal E and constant potential are two views of the same equilibrium condition.
Common Mistake
The field does not increase with depth inside an ideal conductor.
Quick Revision
Electrostatic Equilibrium in Conductors is linked with Conductors, Electrostatics and Electromagnetic Fields. Zero internal E and constant potential are two views of the same equilibrium condition.
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