The figure below shows two circular regions R₁ and R₂ with radii r₁ = 21.8 cm and r₂ = 30.9 cm. In R₁ there is a uniform magnetic field of magnitude B₁ = 50.4 mT directed into the page, and in R₂ there is a uniform magnetic field of magnitude B₂ = 77.9 mT directed out of the page (ignore fringing). Both fields are decreasing at the rate of 10.5 mT/s. Calculated for (a) path 1, (b) path 2, and (c) path 3. (a) Number i (b) Number i (c) Number i ! Units -Path 3, -Path 1 mV ! Units mV ! Units mV Path 2 V

The figure shows three infinitely long wires that carry currents directly into or out of the plane of the figure, as indicated. What is the magnitude (T) of the net magnetic field at the origin? i₁=5.00 A, i2=2.00 A, i3-7.00 A, and d = 2.00 m. d d X

A flat, 173 turn current-carrying loop is immersed in a uniform magnetic field. The area of the loop is 6.37 x 10-4 m2, and the angle between its magnetic dipole moment and the field is 55.9°. Find the strength B of the magnetic field that causes a torque of 1.49 × 10³ N-m to act on the loop when a current of 0.00381 A flows in it. B =

Problem 10: A magnetic needle with magnetic moment μ-0.065 Am2 is placed in a uniform magnetic field B0.65 T as shown in the figure. The angle between the direction of the magnetic moment and the direction of the magnetic field is θ 250 Randomized Variables μ= 0.065 Arn B- 0.65T θ 250 Δ Part (a) Express the potential energy U in terms oft, B, θ. | cos(p) sin(p) | cos(α) sin(a) cos(0) sin(0) ( HOMI 4 5 6 BACKSPACE CLEAR Submit Hint I give up! Hints: 1% deduction per hint. Hints remaining: 1 Feedback: 1% deduction per feedback. Part (b) Calculate the numerical value of U in J. Part (c) If θ can be changed, which value has the minimum potential energy? Part (d) If θ can be changed, which value has the maximum potential energy in degrees? Δ Part (e) Ignore the mass of the needle, express the work needed to change the angle from θ to α in terms oftı, B, θ, α Part (f) If α-1500, calculate the numerical value of the work in J.