A closed loop of `vecB` is produced by a changing electric field. Does it necessarily mean that `vecE` and `dvecE//dt` are non-zero at all points on the loop and in the area enclosed by the loop?
A closed loop of `vecB` is produced by a changing electric field. Does it necessarily mean that `vecE` and `dvecE//dt` are non-zero at all points on the loop and in the area enclosed by the loop?
Text Solution
AI Generated Solution
To address the question, we need to analyze the relationship between the changing electric field and the induced magnetic field in the context of electromagnetic theory.
### Step-by-Step Solution:
1. **Understanding the Concept**:
- According to Faraday's law of electromagnetic induction, a changing electric field can induce a magnetic field. This is expressed mathematically as:
\[
\vec{B} = -\frac{d\Phi_E}{dt}
...
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If you find closed loops of vecB in a region in space, does it necessarily mean that actual charges are flowing across the area bounded by the loops ?
(a) A closed loop is held stationary in the magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets? (b) A closed loop moves normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop (i) when it is wholly inside the region between the capacitor plates (ii) when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop. (c) A rectangular loop and a circular loop are moving out of a uniform magnetic field region (Fig. 6.8) to a field-free region with a constant velocity v. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops. (d) Predict the polarity of the capacitor in the situation described by Fig. 6.9.
Knowledge Check
It is known to you that ''whenever the flux of a magnetic field through the area bound by a closed conducting loop changes , an emf is produced in the loop . Then emf is given by epsi = -(dphi)/(dt) , where psi = int vecB dot "vecds is the flux of the magnetic flux through a closed loop changes, an electric current results. Let us now investigate " what is the external mechanism that maintains the electric field in the loop to drive the current". In the words what is the mechanism to produce an emf? (a) keeping ther magnetic field constant as time pases and moving whole as part of the loop. (b) Keeping the loop at rest and changing the magnetic field. (c) Combination of (a) and (b)that is by moving the loop ( partly or wholly) as well as by changing the field. The mechanism (a) for production of emf is studie under the heating motional emf and mechanism (b) under the heating induced electric field. In mechanism (a) , magnitude of the potential difference across the conductor is given by epsi=Blv where,B,l, v have their usual meanings and the electrostatic field developed within the conductor E=vB Whereas if the magnetic field through a stationary conduting loop is changing with time, then also there will be an induced emf whose value will be epsi=ointvecE.vecdl , where E is the induced electric field. The electric field produced by the changing magnetic field is non-electrostatic and non-conservation If the above magnetic field is present perpendicular to a ring of radius of 1 cm, mass=10 gram and charge =1 C, then the angular velocity of the ring as a function of time is ( the ring and the cylinderical region are coaxial)
It is known to you that ''whenever the flux of a magnetic field through the area bound by a closed conducting loop changes , an emf is produced in the loop . Then emf is given by epsi = -(dphi)/(dt) , where psi = int vecB dot "vecds is the flux of the magnetic flux through a closed loop changes, an electric current results. Let us now investigate " what is the external mechanism that maintains the electric field in the loop to drive the current". In the words what is the mechanism to produce an emf? (a) keeping ther magnetic field constant as time pases and moving whole as part of the loop. (b) Keeping the loop at rest and changing the magnetic field. (c) Combination of (a) and (b)that is by moving the loop ( partly or wholly) as well as by changing the field. The mechanism (a) for production of emf is studie under the heating motional emf and mechanism (b) under the heating induced electric field. In mechanism (a) , magnitude of the potential difference across the conductor is given by epsi=Blv where,B,l, v have their usual meanings and the electrostatic field developed within the conductor E=vB Whereas if the magnetic field through a stationary conduting loop is changing with time, then also there will be an induced emf whose value will be epsi=ointvecE.vecdl , where E is the induced electric field. The electric field produced by the changing magnetic field is non-electrostatic and non-conservation If the above magnetic field is present perpendicular to a ring of radius of 1 cm, mass=10 gram and charge =1 C, then the angular velocity of the ring as a function of time is ( the ring and the cylinderical region are coaxial)
A
`(6t^(2)+12)xx10^(2)` rad/s
B
`(3t^(2)+24)xx10^(2)` rad/s
C
`(t^(2)+12t)xx10^(2)` rad/s
D
`(3t^(2)+4)xx10^(2)` rad/s
Suppose an isolated north pole is kept at the centre of a circlar loop carrying a electric current i. The magnetic field due to the north pole at a point on the periphery of the wire is B. The radius of the loop is a . The force on the wire is
Suppose an isolated north pole is kept at the centre of a circlar loop carrying a electric current i. The magnetic field due to the north pole at a point on the periphery of the wire is B. The radius of the loop is a . The force on the wire is
A
Nearly `2 pi a I B` perpendicular to the plane of the wire
B
`2pi a I B` in the plane of the wire
C
`pi aiB` along the axis of the wire
D
zero
An electric current can be produced in a closed loop
An electric current can be produced in a closed loop
A
by connecting it to a battery, but not by moving a magnet near it
B
By moving a magnet near the loop, but not by connecting a battery
C
By connecting it to a battery, as well as by moving a magnet near it
D
neither by connecting a battery nor by moving a magnet near it
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