A bar of length L = 0.33 m is placed on metallic rails in such a way that a circuit with resistance R = 31.0 2 is formed. At time t = 0 s the length of the rails is x; = 0.17 m. The bar is moving to the right (+x direction) with constant speed v = 0.10 m/s. The rail is placed in a magnetic field B(t) :-0.030t k, where t is in seconds. X X X X X X X X X t > 0 s X AX L B(t) What is the absolute value of the EMF induced in the circuit at time t = 0.60 s? Hints:

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.

A positively charged particle of mass 6.82 x 10-8 kg is traveling due east with a speed of 64.2 m/s and enters a 0.397-T uniform magnetic field. The particle moves through one-quarter of a circle in a time of 4.06 × 10-³ s, at which time it leaves the field heading due south. All during the motion the particle moves perpendicular to the magnetic field. (a) What is the magnitude of the magnetic force acting on the particle? (b) Determine the magnitude of its charge. (a) Number (b) Number pi i Units Units V < B (out of screen)

An aluminum bar of length l = 7.00 cm slides along metal rails through a magnetic field B = 2.40 T. The switch closes at t = 0 s, while the bar is at rest, and a battery of emf εbat = 4.16 V starts a current flowing around the loop. Solve for the terminal velocity if the battery has an internal resistance r = 0.240 Ω and the resistance of the rails and the bar are negligible.