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A long , hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Moth the cylinders are initially electrically neutral
- a)No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
- b)A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
- c)No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinder.
- d)A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
Correct answer is option 'D'. Can you explain this answer?
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A long , hollow conducting cylinder is kept coaxially inside another l...
Explanation:
The given problem involves two long, hollow cylinders, one kept inside the other. Both the cylinders are made of conducting material and are initially electrically neutral.
When a charge density is given to one or both of the cylinders, it can lead to the appearance of a potential difference between them. However, the nature of this potential difference depends on various factors such as the location and distribution of the charges.
Let's consider each option one by one to understand why the correct answer is option 'D'.
a) No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
If the same charge density is given to both the cylinders, then the net charge on each cylinder will be the same. Since both cylinders are made of conducting material, the charges will distribute themselves uniformly on the surfaces of the cylinders. In this case, there will be no potential difference between the two cylinders, as the charges on both cylinders are distributed uniformly and symmetrically.
b) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
If a charge density is given only to the outer cylinder, then the charges will distribute themselves uniformly on the surface of the outer cylinder. However, there will be no charges on the inner cylinder initially. Due to the presence of the outer cylinder, a redistribution of charges will occur in the inner cylinder as well. This redistribution will result in a potential difference between the two cylinders.
c) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinder.
If a uniform line charge is kept along the axis of the cylinders, then the charges will distribute themselves uniformly on the surface of both cylinders. However, since the charges are uniformly distributed along the axis, there will be no potential difference between the cylinders.
d) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
If a charge density is given only to the inner cylinder, then the charges will distribute themselves uniformly on the surface of the inner cylinder. However, there will be no charges on the outer cylinder initially. Due to the presence of the inner cylinder, a redistribution of charges will occur in the outer cylinder as well. This redistribution will result in a potential difference between the two cylinders.
Therefore, the correct answer is option 'D', as a potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
The given problem involves two long, hollow cylinders, one kept inside the other. Both the cylinders are made of conducting material and are initially electrically neutral.
When a charge density is given to one or both of the cylinders, it can lead to the appearance of a potential difference between them. However, the nature of this potential difference depends on various factors such as the location and distribution of the charges.
Let's consider each option one by one to understand why the correct answer is option 'D'.
a) No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
If the same charge density is given to both the cylinders, then the net charge on each cylinder will be the same. Since both cylinders are made of conducting material, the charges will distribute themselves uniformly on the surfaces of the cylinders. In this case, there will be no potential difference between the two cylinders, as the charges on both cylinders are distributed uniformly and symmetrically.
b) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
If a charge density is given only to the outer cylinder, then the charges will distribute themselves uniformly on the surface of the outer cylinder. However, there will be no charges on the inner cylinder initially. Due to the presence of the outer cylinder, a redistribution of charges will occur in the inner cylinder as well. This redistribution will result in a potential difference between the two cylinders.
c) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinder.
If a uniform line charge is kept along the axis of the cylinders, then the charges will distribute themselves uniformly on the surface of both cylinders. However, since the charges are uniformly distributed along the axis, there will be no potential difference between the cylinders.
d) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
If a charge density is given only to the inner cylinder, then the charges will distribute themselves uniformly on the surface of the inner cylinder. However, there will be no charges on the outer cylinder initially. Due to the presence of the inner cylinder, a redistribution of charges will occur in the outer cylinder as well. This redistribution will result in a potential difference between the two cylinders.
Therefore, the correct answer is option 'D', as a potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
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Community Answer
A long , hollow conducting cylinder is kept coaxially inside another l...
When a inner cylinder is charged, both negative and positive charges are induced on the outer cylinder. Using a gaussian enclosing only the inner surface, a radically symmetric electric field exists.
Hence a non-zero potential difference exists.
When outer cylinder is charged, no charges are induced on inner cylinder and hence no electric field exists in between. Potential at all places inside the outer cylinder is constant and hence no potential difference.
Since in (C) and (D) a net charge exists inside a gaussian surface as chosen earlier, electric field and hence potential difference exists.
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A long , hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Moth the cylinders are initially electrically neutrala)No potential difference appears between the two cylinders when same charge density is given to both the cylinders.b)A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.c)No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinder.d)A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.Correct answer is option 'D'. Can you explain this answer?
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