Suora johdin kulkee 2.6 cm:n matkan homogeenisessa magneettikentässä (B = 0.41 T). Johdin on kenttää vastaan kohtisuorassa. Kuinka suuri virta johtimessa on kuljettava, jotta johtimeen kohdistuisi 702 millinewtonin nostovoima? Anna vastaus ampeereina yhden desimaalin tarkkuudella.A straight electric wire is 2.6 cm long distance in a homogenic magnetic field (B = 0.41 T). The wire is perpendicular to magnetic field. What is the current in the wire if there is 702 mN force acting to wire. Give the answer in A with one decimal accuracy.

Question

BlackTom AI · Accepted Answer

We start by restating the givens and the physical setup to ensure clarity about the problem. A straight wire of length L = 2.6 cm = 0.026 m sits in a uniform magnetic field B = 0.41 T, perpendicular to the field. The magnetic force on a current-carrying wire is given by F = I L B sin(theta). Since the wire is perpendicular to the field, theta = 90°, and sin(theta) = 1, simplifying the relation to F = I L B.

Next, we identify the quantities to find the current: the force F is 702 mN = 0.702 N, and the length L and field B are as above. We solve for the current: I = F / (L B).

Compute the denominator first: L B = 0.026 m × 0.41 T = 0.01066 (units: m·T, which matches the N·s·C⁻¹ units in the formula when combined with F in newtons). Then divide the force by this product: I = 0.702 N / 0.01066 ≈ 65.87 A.

Rounding to one decimal place as requested gives I ≈ 65.9 A.

Potential pitfalls to avoid: ensure the length used is the actual length of the wire segment in the magnetic field (0.026 m here), confirm that the angle between current and magnetic field is 90° (which makes sin(theta) = 1), and convert milli-Newtons and milliamperes correctly (0.702 N from 702 mN).

In another phrasing: rewrite the core formula as I = F / (L B). Substituting F = 0.702 N, L = 0.026 m, B = 0.41 T yields I = 0.702 / (0.026 × 0.41) = 0.702 / 0.01066 ≈ 65.87 A, which rounds to 65.9 A.

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