Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densi…

Question

Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them? [NEET 2019]

Accepted Answer

Correct answer: D. (d) Surface charge density, = Charge Area= QA orQ= σA Q_P= 4 R^2=4 πσR^2 … (i ) andQ_Q= 4 (2R )^2=16 πσR^2 … ( ii ) When they are brought in contact with each other, the total charge will be Q_t=Q_P+Q_Q =4 πσR^2+16 πσR^2 [ From Eqs . (i ) and ( ii ) ] =20 πσR^2 … ( iii ) When two charged bodies are connected ∴V_1=V_2 Q_P4 _0R= Q_Q4 _02R ⇒ Q_PR= Q_Q2R ⇒ Q_PQ_Q= 12 ∴Q_P^ '= 13Q_t andQ_Q^ '= 23Q_t After separation, the new surface charge densities on P and Q will be _P= Q_P^ ' Area= 13 Q_t Area ⇒ _1= 13 20 πσR^24 R^2= 53 ( ∵ _P= _1) and _Q= Q_Q^ ' Area= 23 Q_t Area ⇒ _2= 23 20 πσR^24 (2R )^2( ∵ _Q= _2) = 23 54 = 56

$Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them? [NEET 2019]$

Solution

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