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A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is?
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A spatially uniform time dependent magnetic field is changing with tim...
Understanding the Scenario
In this scenario, a unit positive charge is moving in a circular path of radius \( R = 2 \, \text{m} \) perpendicular to a time-dependent magnetic field that changes at a rate of \( 1 \, \text{T/s} \).
Magnetic Field and Charge Interaction
- A changing magnetic field induces an electric field according to Faraday's law of electromagnetic induction.
- The induced electric field \( E \) can be determined using the equation:
\[
E = -\frac{d\Phi_B}{dt}
\]
- Here, \( \Phi_B \) is the magnetic flux given by \( \Phi_B = B \cdot A \), where \( A \) is the area enclosed by the circular path.
Calculating the Induced Electric Field
- The area \( A \) of the circle is calculated as:
\[
A = \pi R^2 = \pi (2)^2 = 4\pi \, \text{m}^2
\]
- Since the magnetic field changes at \( 1 \, \text{T/s} \), the induced electric field becomes:
\[
E = 1 \, \text{T/s} \cdot A = 1 \cdot 4\pi = 4\pi \, \text{V/m}
\]
Work Done on the Charge
- The work done \( W \) on a charge \( q \) moving in an electric field \( E \) over a distance \( d \) is given by:
\[
W = qEd
\]
- For one complete revolution, \( d \) is equal to the circumference of the circle:
\[
d = 2\pi R = 2\pi \cdot 2 = 4\pi \, \text{m}
\]
- Substituting \( q = 1 \, \text{C} \), \( E = 4\pi \, \text{V/m} \), and \( d = 4\pi \, \text{m} \):
\[
W = 1 \cdot 4\pi \cdot 4\pi = 16\pi^2 \, \text{J}
\]
Conclusion
- The magnitude of the work done on the unit positive charge for one complete revolution is \( 16\pi^2 \, \text{J} \).
In this scenario, a unit positive charge is moving in a circular path of radius \( R = 2 \, \text{m} \) perpendicular to a time-dependent magnetic field that changes at a rate of \( 1 \, \text{T/s} \).
Magnetic Field and Charge Interaction
- A changing magnetic field induces an electric field according to Faraday's law of electromagnetic induction.
- The induced electric field \( E \) can be determined using the equation:
\[
E = -\frac{d\Phi_B}{dt}
\]
- Here, \( \Phi_B \) is the magnetic flux given by \( \Phi_B = B \cdot A \), where \( A \) is the area enclosed by the circular path.
Calculating the Induced Electric Field
- The area \( A \) of the circle is calculated as:
\[
A = \pi R^2 = \pi (2)^2 = 4\pi \, \text{m}^2
\]
- Since the magnetic field changes at \( 1 \, \text{T/s} \), the induced electric field becomes:
\[
E = 1 \, \text{T/s} \cdot A = 1 \cdot 4\pi = 4\pi \, \text{V/m}
\]
Work Done on the Charge
- The work done \( W \) on a charge \( q \) moving in an electric field \( E \) over a distance \( d \) is given by:
\[
W = qEd
\]
- For one complete revolution, \( d \) is equal to the circumference of the circle:
\[
d = 2\pi R = 2\pi \cdot 2 = 4\pi \, \text{m}
\]
- Substituting \( q = 1 \, \text{C} \), \( E = 4\pi \, \text{V/m} \), and \( d = 4\pi \, \text{m} \):
\[
W = 1 \cdot 4\pi \cdot 4\pi = 16\pi^2 \, \text{J}
\]
Conclusion
- The magnitude of the work done on the unit positive charge for one complete revolution is \( 16\pi^2 \, \text{J} \).
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A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is?
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A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is?.
A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spatially uniform time dependent magnetic field is changing with time at a constant rate of one tesla per second a unit positive charge is move around the circle of radius R is equals to 2 m perpendicular to this field the magnitude of the work done on charge for one complete revolution is?.
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