Question

2.
Two conducting sphere A and B of radii 10 cm and 30 cm
are charged with charge of – 20 uC and 80 uC respectively.
These spheres are brought into contact, then what will happen​

Answer 1

Solution :

⏭ Given:

✏ Radius of sphere A = 10cm

✏ Radius of sphere B = 30cm

✏ Charge on sphere A = -20uC

✏ Charge on sphere B = +80uC

⏭ To Find:

✏ Charge on each sphere after contact

⏭ Concept:

✏ This question is completely based on concept of 'charge conservation.'

⏭ Assumption:

✏ Radius of sphere A = R1

✏ Radius of sphere B = R2

• Before contact

✏ Charge on sphere A = q1

✏ Charge on sphere B = q2

• After contact

✏ Charge on sphere A = Q1

✏ Charge on sphere B = Q2

✏ Total charge = Q = q1 + q2 = 80-20 = 60uC

⏭ Calculation:

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• Charge on sphere-A

$\implies\sf\:Q1 = \dfrac{Q\times R1}{R1+R2}\\ \\ \implies\sf\:Q1=\dfrac{60\times 10}{10+30}\\ \\ \implies\sf\:Q1=\dfrac{600}{40}\\ \\ \implies\:\boxed{\sf{\pink{\large{Q1 = 15\: uC}}}}$

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• Charge on sphere-B

$\mapsto\sf\:Q2=\dfrac{Q\times R2}{R1+R2}\\ \\ \mapsto\sf\:Q2=\dfrac{60\times 30}{10+30}\\ \\ \mapsto\sf\:Q2=\dfrac{1800}{40}\\ \\ \mapsto\:\boxed{\sf{\orange{Q2=45\:uC}}}$

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• As per charge conservation law :

✏ Total charge before contact = -20 + 80 = 60uC

✏ Total charge after contact = 15 + 45 = 60uC

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