Biot-Savart Law and Magnetic Fields

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Questions and Answers

What is the correct value of charge density λ?

  • 1.81ï‚´102 Nm2/C
  • 1.81ï‚´10-8 N/C
  • 1.81ï‚´102 N/C
  • 5 μC/cm (correct)

The magnetic field at the center (O) of the structure carrying 10 Amp is 0.43 Gauss.

False (B)

What is the magnitude of the magnetic field intensity at position O due to the current carrying wire with 5 Amp?

7.85ï‚´10-5 T

The magnetic field at the center of the current carrying structure is ______ T.

<p>1.73ï‚´10-4</p> Signup and view all the answers

Match the following magnetic field measurements with their values:

<p>0.173 Gauss = (i) Magnetic field of current structure 8.66ï‚´10-5 Gauss = (ii) Magnetic field at center O 1.73ï‚´10-4 T = (iii) Magnetic field measurement at O 1.25ï‚´10-4 T = (iv) Magnetic field intensity of 5 Amp</p> Signup and view all the answers

What is the formula to determine the magnetic field B due to an n-sided polygon loop?

<p>$B = \frac{\mu_0 I}{2R}$ (D)</p> Signup and view all the answers

The magnetic field inside a long solenoid is uniform.

<p>True (A)</p> Signup and view all the answers

What indicates that the magnetic field vector B has circulation or vorticity associated with it?

<p>The presence of a steady line current and the application of Ampère's Law.</p> Signup and view all the answers

The magnetic field inside a solenoid can be represented by the formula ______.

<p>$B = \frac{2 \mu_0 I}{4\pi R}$</p> Signup and view all the answers

Match the following terms with their description:

<p>Magnetic Field = Describes the influence a magnetic field exerts on charges in motion Ampère's Law = Relates magnetic field in terms of current through a path Electric Field = Describes the force per unit charge experienced by a charge Solenoid = A coil of wire designed to create a magnetic field when current flows through it</p> Signup and view all the answers

What is the SI unit of magnetic field (B)?

<p>Tesla (B)</p> Signup and view all the answers

The Biot-Savart law can be used to calculate the magnetic field of a steady line current.

<p>True (A)</p> Signup and view all the answers

What is the relationship between Tesla (T) and Gauss?

<p>1 T = 10^4 Gauss</p> Signup and view all the answers

The permeability of free space is denoted as ______.

<p>μ0</p> Signup and view all the answers

What is the expression for the magnetic field due to one side of a current carrying loop where s = R?

<p>B1 = (μ0I/4πR)[Sin(π/4) - Sin(-π/4)] (A)</p> Signup and view all the answers

As n approaches infinity, the expression for magnetic field approaches that of a circular loop.

<p>True (A)</p> Signup and view all the answers

In the case of an infinite wire, what is the value of θ1 and θ2?

<p>θ1 = -π/2, θ2 = π/2</p> Signup and view all the answers

Match the following expressions with their respective scenarios:

<p>B1 = (μ0I/4πR)[Sin(π/n) - Sin(-π/n)] = Magnetic field for one side of an n-sided polygon B = (nμ0I/2πR)Sin(π/n) = Total magnetic field for an n-sided polygon B1 = μ0I/2nR = Magnetic field as n approaches infinity</p> Signup and view all the answers

Flashcards

Biot-Savart Law

A law used to calculate the magnetic field produced by a steady current.

Magnetic Field

A vector field that describes the magnetic influence on moving electric charges and magnetic dipoles.

Steady Current

An electric current that flows continuously in one direction without changes in magnitude or direction.

Permeability of Free Space (μ₀)

A physical constant representing the ability of a vacuum to support a magnetic field.

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Infinite Wire Magnetic Field

The magnetic field surrounding an infinitely long straight wire carrying a constant current, calculated using Biot-Savart Law.

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Calculating Magnetic Field from Loop

The process of determining the magnetic field strength produced by a current-carrying loop by a superposition of magnetic fields of each part of the loop.

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Circular Loop Magnetic Field

The magnetic field inside and outside a current-carrying loop, calculated by summing the magnetic fields generated by infinitesimal segments which forms the loop.

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Magnetic Field Unit (SI)

The SI unit of magnetic field strength is Tesla (T).

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Magnetic field of a long wire

The magnetic field created by a long, straight wire carrying a constant current is inversely proportional to the distance from the wire.

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Magnetic field circulation

A magnetic field has circulation (vorticity), unlike an electric field in electrostatics.

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Solenoid magnetic field

Inside a long solenoid, the magnetic field is uniform.

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Ampere's Law

A law used to calculate magnetic fields due to currents, useful for calculating specific magnetic field distributions.

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Solenoid

A solenoid is a coil of wire that creates a uniform magnetic field when current flows through it.

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Electric Field Strength

The force experienced by a unit positive charge placed at a point in an electric field.

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What is Gauss's Law?

Gauss's Law states that the total electric flux through any closed surface is proportional to the enclosed electric charge.

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Magnetic Field at Center of Wire Loop

The magnetic field at the center of a current carrying square loop with equal sides is calculated using the formula B = (μ₀I√2) / (4πa), where μ₀ is the permeability of free space, I is the current, and a is the side length of the loop.

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Magnetic Field Intensity

The magnetic field intensity at a point due to a current-carrying wire is the force experienced by a unit magnetic pole placed at that point.

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Study Notes

Magnetic Field at Center of Current Carrying Structure

  • The magnetic field at the center (O) of a structure carrying 10 Amp is 0.43 Gauss.
  • The magnetic field intensity at position O due to the current carrying wire with 5 Amp is half of the magnetic field at the center (O) of the structure carrying 10 Amp.
  • The magnetic field at the center of the current carrying structure is 0.215 Gauss.

Magnetic Field of a Polygon Loop

  • The magnetic field B due to an n-sided polygon loop is calculated using the formula: B = (μ₀ * I * n) / (2 * Ï€ * R)
  • Where μ₀ is the permeability of free space, I is the current, n is the number of sides, and R is the radius of the polygon.

Magnetic Field Inside a Solenoid

  • The magnetic field inside a long solenoid is uniform.
  • The magnetic field vector B has circulation or vorticity associated with it, which is indicated by the curl of the magnetic field vector B.
  • The magnetic field inside a solenoid can be represented by the formula: B = μ₀ * n * I
  • Where μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current.

Magnetic Field Units and Constants

  • The SI unit of magnetic field (B) is Tesla (T).
  • The Biot-Savart law can be used to calculate the magnetic field of a steady line current.
  • The relationship between Tesla (T) and Gauss is: 1 Tesla = 10,000 Gauss.
  • The permeability of free space is denoted as μ₀ and its value is 4Ï€ × 10^-7 H/m.

Magnetic Field Due to a Current Carrying Loop

  • The expression for the magnetic field due to one side of a current carrying loop where s = R is: B = (μ₀ * I) / (4Ï€ * R) * (θ1 - θ2)
  • As n approaches infinity, the expression for magnetic field approaches that of a circular loop.

Magnetic Field Due to an Infinite Wire

  • In the case of an infinite wire, the value of θ1 and θ2 is 0 and Ï€ respectively.
  • The expression for the magnetic field due to an infinite wire is: B = (μ₀ * I) / (2Ï€ * r)
  • Where μ₀ is the permeability of free space, I is the current, and r is the distance from the wire.

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