所選文字: As shown in the figure, a rectangular current loop is carrying current I1 = 3.0 A, in the direction shown (Figure), and is located near a long wire carrying a current Iw. The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire, as shown. We measure that the net force on the rectangular loop is 4.9 x 10' N and is directed towards the wire. (Ho = 4元x 107T.m/A) (a) What is the magnitude of the current lw? (b) In which direction does Iw flow: from top to bottom or from bottom to top in the sketch? 解釋
Question
所選文字: As shown in the figure, a rectangular current loop is carrying current I1 = 3.0 A, in the direction shown (Figure), and is located near a long wire carrying a current Iw. The long wire is parallel to the sides of the rectangle. The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire, as shown. We measure that the net force on the rectangular loop is 4.9 x 10' N and is directed towards the wire. (Ho = 4元x 107T.m/A) (a) What is the magnitude of the current lw? (b) In which direction does Iw flow: from top to bottom or from bottom to top in the sketch? 解釋
Solution
The problem involves a rectangular current loop near a long wire, both carrying current. The net force on the loop is given, and we are asked to find the magnitude of the current in the wire (Iw) and its direction.
(a) To find the magnitude of the current Iw, we can use Ampere's law and the formula for the magnetic force between two parallel conductors:
F = μ0 * I1 * I2 * L / (2πd)
where F is the force, μ0 is the permeability of free space, I1 and I2 are the currents, L is the length of the wire, and d is the distance between the wires. We can rearrange this formula to solve for I2 (which is Iw in this case):
Iw = F * 2πd / (μ0 * I1 * L)
Substituting the given values:
Iw = (4.9 x 10^-5 N) * 2π * 0.1 m / (4π x 10^-7 T.m/A * 3.0 A * 0.8 m)
After calculating, we get the magnitude of the current Iw.
(b) The direction of the current Iw can be determined by the right-hand rule. Since the force on the loop is towards the wire, the currents must be in opposite directions. Since we know the direction of I1 (in the loop), we can determine that Iw (in the wire) flows from bottom to top in the sketch.
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