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
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- 7.17 A solid cylindrical wire of radius a carries current Iin the positive z direction. The wire conductivity is radially dependent and is given by a(p) = oop S/m, where o is a constant. The electric field intensity, constant throughout the wire volume, is given by E = E, a. V/m. (a) Find J in terms of Eo, 0o, and p. (b) Find E, in terms of I. (c) Express J in terms of I and other parameters, excluding Eo. (d) Using your part c result, find H inside and outside the wire. (e) Verify your part d result by applying V x H = J.Three long, straight wires are seen end-on in the figure below. The distance between the wires is 0.248 m. Wires A and B carry current f-1-1.78 A, and wire C carries current le-3.22 A. Assume (for example) the only forces exerted on wire A are due to wires B and C. Find the force per unit length exerted on the following (Express your answers in vector form (a) wire A (b) wire b N/m N/mA cylindrical conductor of radius R = 2.12cm carries a current of I = 2.45A along its length; this current is uniformly distributed throughout the cross-section of the conductor. Calculate the magnetic field midway along the radius of the wire (that is, at r = R/2). Calculate the distance beyond the surface of the conductor at which the magnitude of the magnetic field has the same value as the magnitude of the field at r = R/2.
- A hollow cylindrical conductor of inner radius 0.00798 m and outer radius 0.0238 m carries a uniform current of 9.85 A. What is the current enclosed by an Amperian loop of radius 0.0171 m?Figures 4(a) & (b) show two long straight wires carrying currents h = 8.0 A and I2 = 3.0 A placed along the x-axis and carrying currents perpendicular to the xy-plane in the directions shown. The wire carrying the current Ih is placed at the origin [(x,y) = (0,0)] while the wire carrying current I2 is placed at (x,y) = (1.0,0) cm. 4. y I2 I2 х (ст) х (ст) 1 1 (a) (b) Figure 4 (a) Refer to Figure 4(a). Determine the x-coordinate of the point where the magnetic field is zero.Here we have a wire with current I=3.6 A pointing out of the page. Let's draw an Amperian path around that wire as shown in the picture belwo, with side length d=0.4 m and direction indicated by the arrows. What is the magnitude of the quantity ∮B⃗ ⋅dℓ⃗ for that Amperian path, in T*m?
- A vertical straight wire carrying an upward 30 AA current exerts an attractive force per unit length of 7.1×10−4 N/mN/m on a second parallel wire 7.1 cmcm away. What current (magnitude and direction) flows in the second wire?A long, straight wire lies along the x-axis and carries current I = 5 A in the +x-direction. A small particle with mass 0.0000004470 kg and charge 0.0001 C is traveling in the vicinity of the wire. At an instant when the particle is on the y-axis at y = 3.3 m, its acceleration has components ax = -3.7 m/s2 and ay = 1.3 m/s2. At that instant what is the x- component of the velocity. (To save you time, note that the B field from a wire is given as: B = μ0I/(2πr))Question in the attachments
- A rod of mass m and resistance R slides without friction in a horizontal plane, moving on parallel rails as shown in figure. The rails are separated by a distance d. A battery that maintains a constant emf ε is connected between the rails, and a constant magnetic field B is directed out of the page. Assuming the rod starts from rest at time t = 0, find its velocity in terms of time t, ε, B, d, m, and R.The use of superconductors has been proposed for power transmission lines. A single coaxial cable (as shown) could carry a power of 1.00 × 103 MW (the output of a large power plant) at 200 kV, DC, over a distance of 1.00 × 103 km without loss. An inner wire of radius a = 2.00 cm, made from the superconductor Nb3Sn, carries the current Iin one direction. A surrounding superconducting cylinder of radius b = 5.00 cm would carry the return current I. In such a system, what is the magnetic field (a) at the surface of the inner conductor and (b) at the inner surface of the outer conductor? (c) How much energy would be stored in the magnetic field in the space between the conductors in a 1.00 × 103 km superconducting line? (d) What is the pressure exerted on the outer conductor due to the current in the inner conductor?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.