A charged particle of mass 1 Kg and charge 1 C travels in a uniform magnetic field B=5â, T. If the initial position and velocity of the particle are F(1)= (0,0,0) m v=(1,0,0) m/s respectively, calculate the velocity v(t =1s).
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- Problem 2: An electric current I0.85 A is flowing in a long wire. Consider a rectangular area with one side parallel to the wire and at a distance 0.043 m away from the wire. Let the dimensions of the rectangle be a 0.024 m and b-0.057 m Part (a) Express the magnitude of the magnetic field generated by the wire B at a distance r in terms of I and r. B(r) Но 4 5 6 BACKSPAC CLEAR Submit Hint I give up! Hints: 1% deduction per hint. Hints remaining: 3 Feedback: 1% deduction per feedback. Part (b) Express the magnetic flux, ф, in the rectangle as an integral of B(r) A Part (c) Integrate the expression in part (b) 圖 Part (d) Calculate the numerical value of φ in T-m2.In this problem we will use a 3-dimensional Cartesian coordinate system with coordinates x, y and z. In the cylindrical region defined by the inequality x2 + y2 < R2 the magnetic field is zero, while outside the cylindrical region the magnetic field points in the +z direction and has constant magnitude B. From the origin of our coordinate system an electron starts with velocity v0= eBR/m in the positive x direction (here e is the elementary charge and m is the mass of the electron). Sketch the trajectory of the electronand find the period of its motion.Consider the following vector field defined in a simply connected region, K= = axy ex ayx еy + a₂x еz, where ax, ay and az are constants. Determine the requirements on ax, ay and az for K to be (a) a magnetic field (b) an electrostatic field.
- A proton is shown moving at a constant velocity near a very long wire with a steady current I. At that instant, the proton has a velocity voi and it is lying on the xy-plane at a distance a from the wire. (i, j, k) are the unit vectors in the direction of (+x, +y, +z), respectively +y a I) +Z +X What is the force on the proton during this time? (here e = 1.6 x 10 19 C is the magnitude of the unit charge) HoIevo 2πα Hy Ievo 2πα Ho Ievo -j 2πα Ho levo 2πα -k i -jB x) ☑ ☑ 15 × ☑ ☑ Grade Summary Deductions 0% 100% Potential Submissions Attempt(s) Remaining: 3 4% Deduction per Attempt detailed view Part (a) Three-dimensional axes have been placed to the right of the two-dimensional diagram to assist with three-dimensional visualization of the right-hand images. To indicate the appropriate application of the right-hand rule to obtain the direction of the cross product, v × B, drag an image of the right hand to the target area to the right of those unlabeled axes. Hint: If you hold your right hand in the same orientation as the hand image under consideration, the task is greatly simplified. palm faces direction of c (output) This may be applied to the force, FM, due to a magnetic field, B, on a particle with charge a moving with velocity v where FM = qvx B Because a cross-product relation is involved, the directions of the velocity, the magnetic field, and the magnetic force are related by the right-hand rule to determine the direction of the cross…Let v the velocity of a particle in a constant magnetic field B. We wish to decompose v into v = v⊥ + vk where v⊥ is perpendicular to the magnetic field and vk is parallel to it. Derive vector expressions for v⊥ and vk in terms of v and B.