Worksheet: Magnetic Field due to a Constant Current Loop

In this worksheet, we will practice using the Biot–Savart law to determine the magnitude of the magnetic field produced by a loop of current-carrying wire.

Q1:

The current through a circular loop of conducting wire is 6.0 A and the magnitude of the magnetic field at the centre of the loop is 2 . 0 × 1 0 4 T. What is the radius of the loop?

  • A 0.016 m
  • B 0.012 m
  • C 0.022 m
  • D 0.019 m
  • E 0.025 m

Q2:

A flat, circular loop has 20 turns. The radius of the loop is 10.0 cm and the current through the wire is 0.50 A.

Determine the magnitude of the magnetic field at the centre of the loop.

  • A 4 . 5 × 1 0 5 T
  • B 3 . 9 × 1 0 5 T
  • C 5 . 0 × 1 0 5 T
  • D 6 . 3 × 1 0 5 T
  • E 6 . 7 × 1 0 5 T

Q3:

Two flat circular coils, each with radius 𝑅 = 5 0 . 0 c m and wound with 30 turns, are mounted along the same axis so that they are parallel and 1.5 m apart. What is the magnitude of the magnetic field at the center of either coil at the common axis if a current 𝐼 = 4 0 A flows in the same direction through each coil?

  • A 6 5 × 1 0 3 T
  • B 2 3 × 1 0 3 T
  • C 6 . 3 × 1 0 3 T
  • D 1 . 6 × 1 0 3 T
  • E 1 1 × 1 0 3 T

Q4:

A circular loop of radius 50 cm carries a current 𝐼 . At what distance along the axis of the loop is the magnetic field one half its value at the center of the loop?

Q5:

How many turns must be wound on a flat circular coil of radius 40.0 cm in order to produce a magnetic field of magnitude 4 . 5 × 1 0 5 T at the center of the coil when the current through it is 0.95 A?

Q6:

A charge of 8.0 µC is distributed uniformly around a thin ring of insulating material. The ring has a radius of 0.50 m and rotates at 5 . 0 × 1 0 4 rpm around the axis that passes through its center and is perpendicular to the plane of the ring. What is the magnitude of the magnetic field at the center of the ring?

  • A 1 . 8 × 1 0 9 T
  • B 3 . 2 × 1 0 9 T
  • C 6 . 3 × 1 0 9 T
  • D 1 . 3 × 1 0 9 T
  • E 4 . 8 × 1 0 9 T

Q7:

A thin, non-conducting ring of radius 50 cm is free to rotate around the axis that passes through its center. The ring is charged uniformly with a total charge of 10 µC. If the ring rotates at a constant angular velocity 5 . 0 × 1 0 2 rpm, calculate the magnetic field at a point on its central axis that is a distance 30 cm above the ring.

  • A 2 . 1 × 1 0 1 1 T
  • B 6 3 × 1 0 1 1 T
  • C 1 . 3 × 1 0 1 1 T
  • D 1 . 1 × 1 0 1 1 T
  • E 9 0 × 1 0 1 1 T

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