p'$ inside the sphere at distance ${r_1}$ from the center of the sphere, the magnitude of electric field is :","description":"Practice this DASH question: Let $P\\left( r \\right) = {Q \\over {\\pi {R^4}}}r$ be the change density distribution for a solid sphere of radius $R$ and total cha. Tag details: Electric Charges and Fields: DASH practice topic connected to this question, quiz, and solution; Electric Field: DASH practice topic connected to this question, quiz, and solution; Gauss's Law: DASH practice topic connected to this question, quiz, and solution.","url":"https://learnwithdash.ai/portal/question/789660/","keywords":"Electric Charges and Fields, Electric Field, Gauss's Law, AIEEE, JEE Advanced, JEE Mains, KCET, NCERT, NEET, JEE Main Physics, Class 11 Physics, Class 12 Physics, Physics, Chemistry, Mathematics","about":[{"@type":"Thing","name":"Electric Charges and Fields","description":"Electric Charges and Fields: DASH practice topic connected to this question, quiz, and solution"},{"@type":"Thing","name":"Electric Field","description":"Electric Field: DASH practice topic connected to this question, quiz, and solution"},{"@type":"Thing","name":"Gauss's Law","description":"Gauss's Law: DASH practice topic connected to this question, quiz, and solution"},{"@type":"Thing","name":"AIEEE","description":"AIEEE: DASH practice topic connected to this question, quiz, and solution"},{"@type":"Thing","name":"JEE Advanced","description":"JEE Advanced: JEE Advanced practice topic for deeper concept preparation"},{"@type":"Thing","name":"JEE Mains","description":"JEE Mains: JEE Main practice topic for engineering entrance preparation"},{"@type":"Thing","name":"KCET","description":"KCET: KCET exam practice question for Karnataka entrance preparation"},{"@type":"Thing","name":"NCERT","description":"NCERT: NCERT-aligned concept practice and textbook-based preparation"},{"@type":"Thing","name":"NEET","description":"NEET: NEET exam practice question for medical entrance preparation"},{"@type":"Thing","name":"JEE Main Physics","description":"JEE Main Physics: JEE Main practice topic for engineering entrance preparation"},{"@type":"Thing","name":"Class 11 Physics","description":"Class 11 Physics: Class 11 syllabus topic for board and competitive exam practice"},{"@type":"Thing","name":"Class 12 Physics","description":"Class 12 Physics: Class 12 syllabus topic for board and competitive exam practice"},{"@type":"Thing","name":"Physics","description":"Physics: Physics concept practice with question and solution review"},{"@type":"Thing","name":"Chemistry","description":"Chemistry: Chemistry concept practice with question and solution review"},{"@type":"Thing","name":"Mathematics","description":"Mathematics: Mathematics concept practice with question and solution review"}]}
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Question
Let $P\left( r \right) = {Q \over {\pi {R^4}}}r$ be the change density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $'p'$ inside the sphere at distance ${r_1}$ from the center of the sphere, the magnitude of electric field is :
${Q \over {4\pi \,{ \in _0}\,r_1^2}}$
${{Qr_1^2} \over {4\pi \,{ \in _0}\,{R^4}}}$
${{Qr_1^2} \over {3\pi \,{ \in _0}\,{R^4}}}$
$0$

Solution

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