Magnetostatics: Biot–Savart Law and Ampere’s Circuital Law Quiz Quiz

Assess your understanding of magnetostatics with these questions focusing on the Biot–Savart Law and Ampere’s Circuital Law, covering foundational concepts, applications, and problem-solving techniques for magnetic fields and currents. This quiz helps reinforce core ideas essential for electromagnetism studies and exam preparation.

1. Basic Understanding of Biot–Savart Law

   Which of the following statements correctly describes the Biot–Savart Law when calculating the magnetic field around a thin, straight, current-carrying conductor?

   1. The magnetic field is constant regardless of the distance from the wire.
   2. The magnetic field is proportional to the current and inversely proportional to the distance from the wire.
   3. The magnetic field is proportional to the distance from the wire squared.
   4. The magnetic field is proportional to the current and inversely proportional to the square of the distance from the wire.

   Explanation: The Biot–Savart Law states that the magnetic field at a point due to a current element is proportional to the current and inversely proportional to the distance from the wire, not the square of the distance. The option claiming proportionality to the square of the distance is incorrect because the actual dependency is linear regarding distance. The magnetic field is not constant as one moves away from the wire. The last option misstates the relationship by squaring the distance in the numerator.

2. Application of Ampere’s Circuital Law

   If a long solenoid has 1000 turns per meter and carries a current of 2 A, what is the magnitude of the magnetic field inside the solenoid using Ampere’s Circuital Law (neglecting edge effects)?

   1. 8.00 x 10^-7 T
   2. 2.51 x 10^-3 T
   3. 8.00 x 10^-4 T
   4. 2.51 x 10^-4 T

   Explanation: Inside a solenoid, the magnetic field is given by B = μ₀ n I, where μ₀ is 4π x 10^-7 T·m/A, n is the turn density (1000), and I is the current (2 A). Calculating gives B ≈ 2.51 x 10^-3 T. The option 8.00 x 10^-4 T is too low and results from using incorrect n or I values. 2.51 x 10^-4 T omits a factor of 10, and 8.00 x 10^-7 T uses incorrect units or values. Only 2.51 x 10^-3 T matches the correct calculation.

3. Direction of Magnetic Field Due to Current

   A straight, vertical wire carries a current upwards. At a point located due east of the wire, what is the direction of the magnetic field at that point according to the right-hand rule?

   1. Vertically upward
   2. North
   3. South
   4. Vertically downward

   Explanation: Using the right-hand rule, point your thumb upward along the current, and your curled fingers show the magnetic field circles around the wire. At an eastern point, your fingers point southward. Vertically downward or upward describe the field above or below the wire, not at the side. North is incorrect since that would correspond to the opposite direction of the curl at this location.

4. Comparing Biot–Savart and Ampere’s Law

   For which type of current distribution is Ampere’s Circuital Law most convenient and directly applicable?

   1. A straight, infinite wire
   2. A finite, curved wire segment
   3. A coiled spring with variable turns
   4. A circular loop of wire

   Explanation: Ampere’s Circuital Law is most efficient for systems with pronounced symmetry, like a straight, infinite wire, allowing for easy evaluation of the closed loop integral. While a circular loop can be handled with Biot–Savart Law, Ampere's Law is not generally practical for loops lacking symmetrical fields. A coiled spring with variable turns lacks uniformity, making direct application hard. A finite, curved segment does not satisfy the necessary symmetry for straightforward use of Ampere's Law.

5. Magnetic Field Due to a Circular Current Loop

   Which expression represents the magnetic field at the center of a circular loop of radius r carrying current I?

   1. (μ₀ I r) / 2
   2. (μ₀ I) / (r^2)
   3. (μ₀ I) / (2 r)
   4. (μ₀ I) / (2π r)

   Explanation: For a circular current loop, the magnetic field at the center is (μ₀ I) / (2 r). The first option, (μ₀ I) / (2π r), is for an infinite straight wire. The second option, (μ₀ I r) / 2, incorrectly has r in the numerator, which does not fit the formula for a loop. The fourth option, (μ₀ I) / (r^2), would match a different physical situation or law, such as point-charge fields, not current loops.