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Two hollow conducting spheres of radii R1 and R2 (R1 >>R2) have equal charges. The potential wouldbe :
- a)more on smaller sphere
- b)equal on both the spheres
- c)dependent on the material property of thesphere
- d)more on bigger sphere
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Two hollow conducting spheres of radii R1 and R2 (R1 >>R2) have ...
To find the ratio of the charges, we can use the principle of charge conservation. Since the total charge on the system is zero, the charges on the two spheres must add up to zero.
Let Q1 be the charge on the sphere with radius R1, and Q2 be the charge on the sphere with radius R2.
Q1 + Q2 = 0
We also know that the potential difference between the two spheres is 100 V. The potential difference between two points in an electric field is given by the equation:
V = k(Q1/R1 - Q2/R2)
Where k is the electrostatic constant.
Plugging in the given values:
100 = k(Q1/R1 - Q2/R2)
Since Q1 + Q2 = 0, we can substitute Q2 = -Q1 into the equation:
100 = k(Q1/R1 + Q1/R2)
Rearranging the equation, we get:
Q1/R1 + Q1/R2 = 100/k
Multiplying through by R1*R2, we get:
Q1R2 + Q1R1 = 100R1R2/k
Factoring out Q1, we get:
Q1(R2 + R1) = 100R1R2/k
Dividing both sides by (R2 + R1), we get:
Q1 = 100R1R2/k(R2 + R1)
Similarly, we can find Q2:
Q2 = -Q1 = -100R1R2/k(R2 + R1)
To find the ratio of the charges, we divide Q1 by Q2:
Q1/Q2 = (100R1R2/k(R2 + R1))/(-100R1R2/k(R2 + R1))
The (R2 + R1) and (-100R1R2/k) terms cancel out, leaving:
Q1/Q2 = 1
Therefore, the ratio of the charges on the two spheres is 1:1.
Let Q1 be the charge on the sphere with radius R1, and Q2 be the charge on the sphere with radius R2.
Q1 + Q2 = 0
We also know that the potential difference between the two spheres is 100 V. The potential difference between two points in an electric field is given by the equation:
V = k(Q1/R1 - Q2/R2)
Where k is the electrostatic constant.
Plugging in the given values:
100 = k(Q1/R1 - Q2/R2)
Since Q1 + Q2 = 0, we can substitute Q2 = -Q1 into the equation:
100 = k(Q1/R1 + Q1/R2)
Rearranging the equation, we get:
Q1/R1 + Q1/R2 = 100/k
Multiplying through by R1*R2, we get:
Q1R2 + Q1R1 = 100R1R2/k
Factoring out Q1, we get:
Q1(R2 + R1) = 100R1R2/k
Dividing both sides by (R2 + R1), we get:
Q1 = 100R1R2/k(R2 + R1)
Similarly, we can find Q2:
Q2 = -Q1 = -100R1R2/k(R2 + R1)
To find the ratio of the charges, we divide Q1 by Q2:
Q1/Q2 = (100R1R2/k(R2 + R1))/(-100R1R2/k(R2 + R1))
The (R2 + R1) and (-100R1R2/k) terms cancel out, leaving:
Q1/Q2 = 1
Therefore, the ratio of the charges on the two spheres is 1:1.
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Two hollow conducting spheres of radii R1 and R2 (R1 >>R2) have ...
∴ Potential is more on smaller sphere.
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Two hollow conducting spheres of radii R1 and R2 (R1 >>R2) have equal charges. The potential wouldbe :a)more on smaller sphereb)equal on both the spheresc)dependent on the material property of thesphered)more on bigger sphereCorrect answer is option 'A'. Can you explain this answer?
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