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A: The amperes circuital law is given by
A long, straight wire with a circular cross section of radius R carries a current I. Assume that the current density is not constant across the cross section of the wire, but rather varies as J=αr, where αα is a constant.
Q1. What is the direction of the magnetic field in the two regions given (r < R and r >R) using the Amperian equation.
Image A. What is the direction of the magnetic field at a point P a distance a away from the bend.
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- e. Draw the Amperian loop that will allow you to find the magnetic field at a point P inside the cylinder (r < b). f. Write the integral B ds = $ B cos o ds in terms of the unknown B and the givens 7 and/or b. Your answer should look familiar. g. i. What is the current Ithru going through your Amperian loop? Hint: the current is spread out evenly over the cross-sectional area of the wire so set up a ratio of areas. Check that your expression for Ithrough has the dimensions of current. h. Use (f) and (g) to determine the magnetic field for rA small circular coil of 20 loops of wire having a radius of 1 cm is at rest in the X-y plane (so the normal to the loop points in the +z-direction). A uniform magnetic field of 0.5 T is turned on in the +x-direction. What is the magnetic flux through the loop? a. 7.85 x 10 Tm² b. 1.57 x 10 4 T m² O c. 3.14 x 10 3 T m2 O d. 0 T m2Section Total 20 Electric current in an Score infinitely long straight wire is I. A rectangle with height h and width d is placed beside the wire at the same plane. Left side has a distance of r away from the wire. Using Ampere's law to find the magnetic field distribution and calculate the magnetic Score flux through the rectangle.An electron travels with speed 1.3×107 m/s between the two parallel charged plates shown in the figure. The plates are separated by 1.0 cm and are charged by a 200 V battery. Part A What magnetic field strength will allow the electron to pass between the plates without being deflected?Express your answer in tesla. Part B What is the direction of the magnetic field?A UpB DownC Out of the pageD Into the pageFigure 1: CRT with coils in Helmholtz configuration. The hot cathode emits electrons which are then accelerated through potential difference Vacc. When the electrons enter the magnetic field B, which is perpendicular to their velocity, they move on a circular path with radius r. The magnetic field is due to coils in Helmholtz configuration (2 coils separated distance that equals their radius). The magnetic field due to one of the coils with radius R, at a point on the axis distance z away from the center of the coil, was found using the Biot-Savart law: HOIR?N B1 2(R2 + z2)žN circular loops of conducting wire of radius 3.0 cm carries a current of 10 A. If the magnetic field at the center of the multiple turns of loop is 3.14 x 10-3 T, how many turns of loop are in the conducting coil? a. 15 b. 10 c. 30 d. 20 e. 25only parts d and ea. The circle below represents a Brunton compass. What is the bearing of the following objects with respect to you if the needle of the compass points to the following directions? Express the reading in quadrantal and azimuthal notation. Note that magnetic north is denoted by 0°. Hint: You must first use geometric construction to find the center of the circle. 0° A Direction Quadrantal Azimuthal A В В ETwo long wires, one of which has a semicircular bend of radius R and center P, are positioned as shown below. If both wires carry a current I, how far apart must their parallel sections be so that the total magnetic field at P is zero? Express a in terms of R. Does the current in the straight wire flow up or down? Explain. The infinite, straight wire shown below carries a current I1. The rectangular loop, whose long sides are parallel to the wire, carries a current I2. What are the magnitude and direction of the total magnetic force on the rectangular loop due to the magnetic field of the long wire?4. Figure in the below shows a cross section of a hollow cylindrical conductor of radii a and b, carrying a uniformly distributed current i. a) Show that the magnetic field magnitude B(r) for the radial distance rin the range. bc) with a current of I in the opposite direction (Figure 2). Assume that the currents are distributed uniformly over the cross sections of each conductor. i. Derive an expression for the magnitude and direction of the magnetic field at point a c. What is the advantage of using the coaxial cable as compared to a long straight wire? a b С Figure 2j ust A please!