UPSC Exam > UPSC Questions > 3.8 Inside or outside ** A setup consists of ...
Start Learning for Free
3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).
However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P?
However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P?
Most Upvoted Answer
3.8 Inside or outside ** A setup consists of a spherical metal shell a...
Understanding Electric Fields in Spherical Shells
The scenario revolves around a point charge and its interaction with a spherical metal shell, leading to distinct electric field behaviors depending on the configuration.
Field Behavior Inside the Shell
- When the spherical shell is positioned around point P with the charge q outside, the electric field at point P is zero.
- This result arises from the uniqueness theorem, which states that the electric field inside a conductor in electrostatic equilibrium is zero.
Transitioning to Outside the Shell
- As we increase the size of shell A, we can visualize a continuous transition.
- When the left part of the shell becomes an infinite plane, it effectively behaves like an infinite sheet of charge.
- This infinite plane creates a uniform electric field on one side, allowing us to shift from a zero field to a nonzero field at point P.
Field Behavior Outside the Shell
- In position B, with the shell encompassing the charge q, point P exists outside the shell.
- Here, the electric field is nonzero due to the influence of charge q, which now affects the region outside the shell.
Key Insight
- The transition from zero electric field to a nonzero field at point P highlights the fundamental principle of electric fields being influenced by surrounding charges.
- The continuity of the electric field is maintained, demonstrating how changes in geometry and charge distribution can alter field characteristics.
In summary, the electric field's behavior is contingent upon the configuration of charges and the boundaries imposed by conductors, leading to a fascinating interplay of electrostatics.
The scenario revolves around a point charge and its interaction with a spherical metal shell, leading to distinct electric field behaviors depending on the configuration.
Field Behavior Inside the Shell
- When the spherical shell is positioned around point P with the charge q outside, the electric field at point P is zero.
- This result arises from the uniqueness theorem, which states that the electric field inside a conductor in electrostatic equilibrium is zero.
Transitioning to Outside the Shell
- As we increase the size of shell A, we can visualize a continuous transition.
- When the left part of the shell becomes an infinite plane, it effectively behaves like an infinite sheet of charge.
- This infinite plane creates a uniform electric field on one side, allowing us to shift from a zero field to a nonzero field at point P.
Field Behavior Outside the Shell
- In position B, with the shell encompassing the charge q, point P exists outside the shell.
- Here, the electric field is nonzero due to the influence of charge q, which now affects the region outside the shell.
Key Insight
- The transition from zero electric field to a nonzero field at point P highlights the fundamental principle of electric fields being influenced by surrounding charges.
- The continuity of the electric field is maintained, demonstrating how changes in geometry and charge distribution can alter field characteristics.
In summary, the electric field's behavior is contingent upon the configuration of charges and the boundaries imposed by conductors, leading to a fascinating interplay of electrostatics.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P?
Question Description
3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P?.
3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P?.
Solutions for 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? defined & explained in the simplest way possible. Besides giving the explanation of
3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P?, a detailed solution for 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? has been provided alongside types of 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? theory, EduRev gives you an
ample number of questions to practice 3.8 Inside or outside ** A setup consists of a spherical metal shell and a point charge q. We are interested in the electric field at a given point P. In Fig. 3.24(a), if the shell is placed in position A around point P, with the charge q outside, then we know that the field at P is zero by the uniqueness theorem. On the other hand, if the shell is placed in position B around the charge q, with point P outside, then we know that the field at P is nonzero (see the example in Section 3.2).However, we can transition continuously from one of these cases to the other by increasing the size of shell A until the left part of it becomes an infinite plane between q and P, and then con- sidering this plane to be the right part of an infinite shell B, and then shrinking this shell down to the given size. During this pro- cess the point P goes from being inside the shell to being outside. What's going on here? How can we transition from zero field to nonzero field at point P? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup