A 21 cm long metal rod is oriented horizontally in a uniform magnetic field with magnetic flux density of 571 G. The magnetic field is directed vertically down into the ground. A current of 12 A is passed through the rod. Neglect the magnetic field of earth at the location of this apparatus.

Determine the magnitude of magnetic force on the rod in the units of N.

Write your answer in decimal form with three digits to the right of the decimal point (e.g. 5.374); do not write any units.

Question

A 21 cm long metal rod is oriented horizontally in a uniform magnetic field with magnetic flux density of 571 G. The magnetic field is directed vertically down into the ground. A current of 12 A is passed through the rod. Neglect the magnetic field of earth at the location of this apparatus.

Determine the magnitude of magnetic force on the rod in the units of N.

Write your answer in decimal form with three digits to the right of the decimal point (e.g. 5.374); do not write any units.

BlackTom AI · Accepted Answer

We start by identifying the formula for the magnetic force on a straight current-carrying conductor in a uniform magnetic field: F = I L B sin(theta), where theta is the angle between the current direction and the magnetic field.

- In this setup, the rod is horizontal and the magnetic field is vertical, so the angle between the current direction (along the rod) and B is 90 degrees. Thus sin(theta) = 1, and F = I L B.

- Convert the given quantities to SI units:
  - Current I = 12 A (already in SI units)
  - Length L = 21 cm = 0.21 m
  - Magnetic flux density B = 571 G. Since 1 G = 1e-4 T, B = 571 × 1e-4 T = 0.0571 T

- Compute the force: F = I L B = 12 × 0.21 × 0.0571. First, 12 × 0.21 = 2.52. Then 2.52 × 0.0571 ≈ 0.143892 N.

- Rounding to three decimal places as requested gives 0.144. Since the prompt asks for the numeric value without units and to three decimals, this is the appropriate form.

Note on options: there are no answer choices provided in the prompt to evaluate for correctness or incorrect reasoning against alternative possibilities. The calculation above directly yields the required magnitude of the magnetic force on the rod.

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