12.4 Ampère’s Law

• What is the mathematical expression for Ampère's Law?

  $\oint \vec{B} \cdot d\vec{l} =$$\mu_{0} I$
• Ampère's Law states that the magnetic field around a closed loop is proportional to the electric current passing through the loop
• The magnetic field is the area around a magnet where magnetic forces are exerted.
• What does the line integral in Ampère's Law equal in terms of μ₀ and I?

  $\mu_{0} I$
• In Ampère's Law, the line integral is denoted as ∮ B ⋅ dl.
• A magnetic field exerts a force on moving charges.
• What is the symbol for the magnetic field in physics?

  B
• The direction of the magnetic field is determined by the right-hand rule.


  True
• What is the unit of the magnetic field vector in Ampère's Law?

  Tesla
• What is the direction of the magnetic field around a straight wire carrying current?

  Concentric circles
• In the line integral, B represents the magnetic field
• In Ampère's Law, \oint \vec{B} \cdot d\vec{l} = \mu_{0} I_{\text{enc}}</latex>, $I_{\text{enc}}$ represents the current enclosed
• Ampère's Law is more efficient for symmetric current distributions than the Biot-Savart Law.


  True
• Ampère's Law is easier to apply than the Biot-Savart
• Ampère's Law states that the magnetic field around a closed loop is proportional to the electric current
• Steps to determine the direction of the magnetic field using the right-hand rule

  1️⃣ Point your thumb in the direction of the current

  2️⃣ Your fingers curl in the direction of the magnetic field
• The magnetic field exerts a force only on moving electric charges
• What is the mathematical expression for Ampère's Law using current enclosed (I_enc)?

  $\oint \vec{B} \cdot d\vec{l} =$$\mu_{0} I_{\text{enc}}$
• Steps to calculate the magnetic field using Ampère's Law for a straight wire with constant current

  1️⃣ Choose a closed loop around the wire

  2️⃣ Apply Ampère's Law to the loop

  3️⃣ Calculate the magnetic field magnitude
• What is the physical interpretation of Ampère's Law?

  Magnetic field around a current
• What condition simplifies the line integral in Ampère's Law for symmetric current distributions?

  Magnetic field is constant
• What is the magnetic field formula for a straight wire carrying current I at a distance r?

  $B =$$\frac{\mu_{0} I}{2\pi r}$
• For a solenoid, the magnetic field is given by $B =$$\mu_{0} n I$, where n is the number of turns per unit length
• The magnetic field vector $\vec{B}$ is measured in units of Tesla
• What happens when an electric current flows through a conductor?

  It produces a magnetic field
• What forms around a straight wire carrying current according to the right-hand rule?

  Concentric circles of magnetic field lines
• What is the unit of the magnetic field?

  Tesla (T)
• Match the symbol with its definition:

  B ↔️ Magnetic field vector

  dl ↔️ Differential length vector

  $\mu_{0}$ ↔️ Permeability of free space

  I ↔️ Total current
• Magnetic field lines always form closed loops.

  True
• The magnetic field is a vector field with both magnitude and direction.


  True
• The magnetic field is produced by moving electric charges
• What does Ampère's Law relate the magnetic field to?

  Electric current
• The permeability of free space, μ₀, is approximately 4π × 10^-7 T⋅m/A.


  True
• The right-hand rule is used to determine the direction of the magnetic field around a current-carrying wire.


  True
• The unit of the magnetic field is Tesla, and the unit of the electric field is Newtons per Coulomb.


  True
• Match the feature with the correct law:

  Symmetric current distributions ↔️ Ampère's Law

  Complex current configurations ↔️ Biot-Savart Law
• Why is Ampère's Law easier to apply for symmetric current distributions?

  Simpler line integral
• Ampère's Law requires symmetry in current distributions to be accurate.


  True
• What is the value of the permeability of free space (μ₀)?

  4π × 10^-7 T⋅m/A
• What shape does the magnetic field form around a straight wire carrying current?

  Concentric circles