Consider two infinitely long and parallel wires separated by distance d and carrying currents I₁ = -1₂. (a) Find the magnitude and direction of the vector potential A(r1, 72) at a point P where r₁ and r2 represent the distances to P from wire 1 and wire 2 respectively. (b) What is the magnitude of A for r₁ = r₂? (c) What is the value of the magnetic field B for r₁ = r₂? (d) Given that B = V x A, how can you reconcile the answers to (b) and (c) above?
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- A long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross section of the conductor but is a function of the radius according to J = 4br2, where b is a constant. Find an expression for the magnetic field magnitude B at the following distances, measured from the axis in part a and b. (Use the following variables as necessary: ?0, r1, r2, b, R.) Note: See image for the original question and figureA loop in the form of an equilateral triangle with side L is in the first quadrant of the xy plane with one of the vertices at the origin and one of the sides on the x axis. Obtain the magnetic force on each side of the triangle if a current I passes through the loop and the applied magnetic field is given by Bo = (Box)i + (Bo)k, with Bo> 0. What is the total force on the loop? Obs: the magnetic field it's not defined in j.In Fig. 2, an electron with an initial kinetic energy of 5.0 keV enters region 1 at time t= 0. That region contains a uniform magnetic field directed into the page, with magnitude 0.010 T. The electron goes through a half circle and then exits region 1, headed toward region 2 across a gap of 25.0 cm. There is an electric potential diference AV= 2000 V across the gap, with a polarity such that the electron's speed increases uniformly as it traverses the gap. Region 2 contains a uniform magnetic field directed out of the page, with magnitude 0.020 T. The elctron goes through a half circle and then leaves region 2. At what time t does it leave? (e= 1.6 × 10-19 C, mẹ = 9.11 × 10-3' kg) Region 1 I av AV Region 2 O B2 Fig. 2
- A positively charged particle slides off a frictionless and smooth surface with initial X X X X X X X X speed v, =v, . It then enters into a region with X X X X X x x x X uniform magnetic field pointing into the page. X X X X x x x x X x x x x x X x x x The particle eventually hits the ground with final speed v, air time and range S · The particle slides off the edge again with identical initial speed, but this time without the magnetic field. The particle then hits the ground with final speed v,, air time t, , and range s,. Determine the relationships between v, and v,, t, and t, , as well as s, and s, (3 marks). Please note that no calculation is needed. You were to provide the relationship in the sense that whether one variable is greater than, smaller than, or equals to the other one (>, <, or =). Provide a rough explanation (3 marks).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.PROBLEM 1. As shown in the figure, a uniform magnetic field B points upward, in the plane of the paper. Then the current is turned on in a long wire perpendicular to the paper. The magnetic field at point 1 is then found to be zero. From this information, draw the magnetic field vector at point 2 when the current is on. Draw the vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. Explain your reasoning. 2• H Wire 1.
- Find the hydrostatic force on one end of a cylindrical drum with radius3 ft if the drum is submerged in water 10 ft deep.A long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross-section of the conductor but is a function of the radius according to J = 2br, where b is a constant? Find an expression for the magnetic field magnitude B at the following distances, measured from the axis. (Use the following variables as necessary: ?0, r1, r2, b, R.) (a) r1 < R (b) r2 > RThe current in a long, straight conductor has the following form:I(t) = I0cos ωtWhat is the magnitude of the magnetic field a distance r away from theconductor?
- Question 1: The magnetic flux of a uniform magnetic field of magnitude B througn a flat area A whose area vector is at angle with the magnetic field is given by ... (select the best choice) OBXA OBA sin OBA OAX B OBA cos Part (a) › analyzes the directions of the forces between two parallel wires carrying currents in the same direction. Perform a similar analysis for the forces between two parallel wires carrying currents in opposite directions. Those forces are... (select the best choice) Orepulsive to the left Part (b) Oto the right Oup Odown O attractive two ways of determining the direction of the magnetic field produced at some point by a moving charge or a current. Which hand or hands are avolved in both ways? (select the best choice) OBoth hands, but mainly the right ORight hand OBoth hands equally OLeft hand ONone of the other choicesA charged particle is entering a squared region of space with a uniform magnetic field. The sides of the region are 6 m wide. The particle enters the region exactly in the middle of one of the sides in a direction perpendicular to it, as in the Figure below. The charge of the particle is q = 20.0μC, its mass is m = 6.0 × 10-¹6 kg, and the velocity of the particle is |v| = 5 × 10³ m/s. How strong is the magnetic field so that the particle escapes such region in a direction perpendicular to the one it entered? See Figure for more details. XX XXXXXX :XXXXXXX XX XXX:The diagram above shows segments of two long straight wires, carrying currents. This time I1 = 6.46, I2 = 2.03 A, and the two wires are separated by 1.10 cm. Now consider the charge q = 6.74 x 10^-6 C, located a distance of 6.31 cm to the right of wire I2, moving to the right at speed v = 43.2 m/s. What is the magnitude of the total magnetic force on this charge? 3.34E-09 N 2.00E-09 N 6.95E-09 N 4.17E-09 N