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A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.?
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A metal bar of length L =10 cm is free to move along a metal guide on ...
Solution:
Given:
- Length of metal bar, L = 10 cm = 0.1 m
- Resistance of rectangle electric circuit, R = 2 Ω
- Non-uniform magnetic field, B(x,t) = c(x-ct), where k = 2 Wb/m³ and c = 3 × 10⁸ m/s
- Speed of the metal bar along x-axis, v = 5 m/s
To find: Expression for electric current in the circuit
Calculation:
1. Magnetic flux through the rectangle circuit
- The magnetic flux through the rectangle circuit is given by Φ = B.A, where B is the magnetic field and A is the area of the rectangle.
- Since the magnetic field is non-uniform, we need to find the magnetic flux for each side of the rectangle separately.
- For the sides AB and CD, the magnetic field is perpendicular to the area, so the magnetic flux is zero.
- For the sides BC and DA, the magnetic field is parallel to the area, so the magnetic flux is given by Φ = B.L, where L is the length of the side.
- Thus, the magnetic flux through the rectangle circuit is Φ = 2B.L = 2cL(x-ct).
2. EMF induced in the circuit
- According to Faraday's law of electromagnetic induction, the EMF induced in the circuit is given by E = -dΦ/dt, where Φ is the magnetic flux through the circuit.
- Differentiating Φ with respect to time t, we get dΦ/dt = 2cL(c - v).
- Substituting the value of dΦ/dt in the above equation, we get the EMF induced in the circuit as E = -2c²L(x - ct).
3. Electric current in the circuit
- According to Ohm's law, the electric current in the circuit is given by I = E/R, where E is the EMF and R is the resistance of the circuit.
- Substituting the values of E and R in the above equation, we get the electric current in the circuit as I = -c²L(x - ct)/R.
Answer:
The expression for electric current in the circuit is I = -c²L(x - ct)/R = -7.5×10¹⁴(x - ct) A.
Given:
- Length of metal bar, L = 10 cm = 0.1 m
- Resistance of rectangle electric circuit, R = 2 Ω
- Non-uniform magnetic field, B(x,t) = c(x-ct), where k = 2 Wb/m³ and c = 3 × 10⁸ m/s
- Speed of the metal bar along x-axis, v = 5 m/s
To find: Expression for electric current in the circuit
Calculation:
1. Magnetic flux through the rectangle circuit
- The magnetic flux through the rectangle circuit is given by Φ = B.A, where B is the magnetic field and A is the area of the rectangle.
- Since the magnetic field is non-uniform, we need to find the magnetic flux for each side of the rectangle separately.
- For the sides AB and CD, the magnetic field is perpendicular to the area, so the magnetic flux is zero.
- For the sides BC and DA, the magnetic field is parallel to the area, so the magnetic flux is given by Φ = B.L, where L is the length of the side.
- Thus, the magnetic flux through the rectangle circuit is Φ = 2B.L = 2cL(x-ct).
2. EMF induced in the circuit
- According to Faraday's law of electromagnetic induction, the EMF induced in the circuit is given by E = -dΦ/dt, where Φ is the magnetic flux through the circuit.
- Differentiating Φ with respect to time t, we get dΦ/dt = 2cL(c - v).
- Substituting the value of dΦ/dt in the above equation, we get the EMF induced in the circuit as E = -2c²L(x - ct).
3. Electric current in the circuit
- According to Ohm's law, the electric current in the circuit is given by I = E/R, where E is the EMF and R is the resistance of the circuit.
- Substituting the values of E and R in the above equation, we get the electric current in the circuit as I = -c²L(x - ct)/R.
Answer:
The expression for electric current in the circuit is I = -c²L(x - ct)/R = -7.5×10¹⁴(x - ct) A.
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A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.?
Question Description
A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.?.
A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.?.
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A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.?, a detailed solution for A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.? has been provided alongside types of A metal bar of length L =10 cm is free to move along a metal guide on a horizontal plane forming a rectangle electric circuit with resistance 2 ohm. There is a non uniform magnetic field in the plane which varies according to the law B(x,t)=c(x-ct) where k=2wb/m^3 c=3.10^8ms. Assume to move bar with constant speed v=5m/s along x ,determine the expression of electric current.? theory, EduRev gives you an
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