You have a circular coil of 40 loops of wire with an area of 0.03 m" that you want to place into a uniform magnetic field with a strength of 0.01 T. A. Make a sketch showing how you would orient the coil inside the magnetic field so that the wire would feel the largest torque if a current were flowing through it. You may choose any direction for the magnetic field, but be sure to clearly indicate the direction of the field in your sketch. [1] B. Add the direction of current flow to your sketch and describe with words or with a labeled arrow in what direction the loop would start to turn if current were flowing in that direction. [1] C. How much current would you need to pass through the wire so that the magnitude of the torque would be 1.5 N?m? [4]
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To orient the coil inside the magnetic field so that it feels the largest torque, we need to align the plane of the coil perpendicular to the direction of the magnetic field. This means that the coil should be placed such that its plane is parallel to the plane of Show more…
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To understand the origin of the torque on a current loop due to the magnetic forces on the current-carrying wires. This problem will show you how to calculate the torque on a magnetic dipole in a uniform magnetic field. We start with a rectangular current loop, the shape of which allows us to calculate the Lorentz forces explicitly. Then we generalize our result. Even if you already know the general formula to solve this problem, you might find it instructive to discover where it comes from. a) Give a more general expression for the magnitude of the torque τ. Rewrite the answer found in Part A in terms of the magnitude of the magnetic dipole moment of the current loop m. Define the angle between the vector perpendicular to the plane of the coil and the magnetic field to be ϕ, noting that this angle is the complement of angle θ in Part A. Give your answer in terms of the magnetic moment m, magnetic field B, and ϕ.
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Consider a rectangular-shaped loop made up of N = 61 closely wrapped turns of wire, as shown in the attached figure. The dimensions of the loop in meters are a = 0.18 m and b = 0.16 m. The coil is hinged, like a door, along the y-axis and the plane of the loop makes an angle, θ = 19°, with the x-axis. What is the magnitude of the torque exerted on the loop, at this angle, if the magnetic field is uniform and is pointed in the x-direction with a value of B = 0.800 T (teslas) and the current in the wire is I = 1.5 A (amperes) and flowing in the direction shown? Calculate the answer in newton·meters (N·m) and round it to two significant figures.
A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.95 A, is oriented with the plane of its loop perpendicular to a uniform 1.50-T magnetic field ($\textbf{Fig. E27.42}$). (a) Calculate the net force and torque that the magnetic field exerts on the coil. (b) The coil is rotated through a 30.0$^\circ$ angle about the axis shown, with the left side coming out of the plane of the figure and the right side going into the plane. Calculate the net force and torque that the magnetic field now exerts on the coil. ($Hint:$ To visualize this three-dimensional problem, make a careful drawing of the coil as viewed along the rotation axis.)
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