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Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a?
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Consider two conce ntric conducting spherical shells with inner and ou...
To have equal surface charge densities on the outer surface of both shells, the following conditions should be satisfied:
1. d > b and c = √2a
Explanation:
- The surface charge density is defined as the total charge divided by the surface area. In order for the surface charge densities to be equal, the total charge on each shell must be the same.
- Let's assume that the inner shell has a charge q1 and the outer shell has a charge q2.
- The surface area of a sphere is given by 4πr^2, where r is the radius.
- The surface area of the inner shell (with radius b) is 4πb^2, and the surface area of the outer shell (with radius d) is 4πd^2.
- Since the charge on both shells is q, we can write the surface charge densities as q1/(4πb^2) and q2/(4πd^2).
Now, let's examine the given conditions:
2. d = 4b and c = 2a
Explanation:
- If d = 4b, then the surface area of the outer shell is 4^2 = 16 times larger than the surface area of the inner shell.
- In order for q2/(4πd^2) to be equal to q1/(4πb^2), the charge on the outer shell (q2) must be 16 times larger than the charge on the inner shell (q1).
- However, the question states that both shells are given the same amount of positive charges (q). Therefore, this condition cannot be satisfied.
3. d = 2b and c > a
Explanation:
- If d = 2b, then the surface area of the outer shell is 2^2 = 4 times larger than the surface area of the inner shell.
- In order for q2/(4πd^2) to be equal to q1/(4πb^2), the charge on the outer shell (q2) must be 4 times larger than the charge on the inner shell (q1).
- This condition can be satisfied by distributing the total charge q between the inner and outer shells in a ratio of 1:4.
- Since c > a, the outer shell has a larger radius and thus a larger surface area. This ensures that the surface charge densities on both shells are equal.
Therefore, the correct answer is d > b and c = √2a.
1. d > b and c = √2a
Explanation:
- The surface charge density is defined as the total charge divided by the surface area. In order for the surface charge densities to be equal, the total charge on each shell must be the same.
- Let's assume that the inner shell has a charge q1 and the outer shell has a charge q2.
- The surface area of a sphere is given by 4πr^2, where r is the radius.
- The surface area of the inner shell (with radius b) is 4πb^2, and the surface area of the outer shell (with radius d) is 4πd^2.
- Since the charge on both shells is q, we can write the surface charge densities as q1/(4πb^2) and q2/(4πd^2).
Now, let's examine the given conditions:
2. d = 4b and c = 2a
Explanation:
- If d = 4b, then the surface area of the outer shell is 4^2 = 16 times larger than the surface area of the inner shell.
- In order for q2/(4πd^2) to be equal to q1/(4πb^2), the charge on the outer shell (q2) must be 16 times larger than the charge on the inner shell (q1).
- However, the question states that both shells are given the same amount of positive charges (q). Therefore, this condition cannot be satisfied.
3. d = 2b and c > a
Explanation:
- If d = 2b, then the surface area of the outer shell is 2^2 = 4 times larger than the surface area of the inner shell.
- In order for q2/(4πd^2) to be equal to q1/(4πb^2), the charge on the outer shell (q2) must be 4 times larger than the charge on the inner shell (q1).
- This condition can be satisfied by distributing the total charge q between the inner and outer shells in a ratio of 1:4.
- Since c > a, the outer shell has a larger radius and thus a larger surface area. This ensures that the surface charge densities on both shells are equal.
Therefore, the correct answer is d > b and c = √2a.
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Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a?
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Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a?.
Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider two conce ntric conducting spherical shells with inner and outer radii a, b and c, d as shown in the figure. Both the shells are given q amount of positive charges. In order to have equal surface charge densities on the outer suface of both the shells, the following conditions should be satisfied. d= 4b and c = 2a d= 2b and c = V2a d = 2b and c > a CORRECT ANSWER d> bandc = V2a?.
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