A wire of infinite length carrying current I=1A having the trajectory as shown in the figure . Find the magnetic field at the point P (1,0,0)
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- The arrangement illustrated in the figure below is composed of six finite straight wires of length l. The electric current flowing in such an arrangement is i. Using the Biot-Savart law, calculate: The magnitude of the magnetic field at point P due to the wire located along segment ab.Two thin circular wires, each with radius a, carry equal currents I but in opposite directions. They are placed so that their centers are at z = ±a/2 and the plane of each loop is parallel to the xy- plane. Find the magnetic field at a point (0, 0, 2) on the symmetry axis. What is the magnetic dipole moment of the system? Expand B(z) for z ≫ a keeping the lowest order term in a/z.A particle of charge +q and mass m moves with velocity v → 0 pointed in the +y-direction as it crosses the x-axis at x = R at a particular time. There is a negative charge –Q fixed at the origin, and there exists a uniform magnetic field B → 0 pointed in the +z-direction. It is found that the particle describes a circle of radius R about –Q. Find B → 0 in terms of the given quantities.
- A particle of mass m, charge q and position x moves in a constant, uniform magnetic field B which points in a horizontal direction. The particle is also under the influence of gravity, g , acting vertically downwards. Write down the equation of motion and show that it is invariant under translations x -> x + x0. Obtain x = \alpha x \times n + gt + a where \alpha = qB/m, n is a unit vector in the direction of B and a is a constant vector. Show that, with a suitable choice of origin, a can be written in the form a = an. By choosing suitable axes, show that the particle undergoes a helical motion with a constant horizontal drift. Suppose that you now wish to eliminate the drift by imposing a uniform electric field E. Determine the direction and magnitude of E. TrainingConsider an infinite hollow conducting cylinder of inner radius R and outer radius 3R, as shown. The non-uniform current density J is out of the page and varies with distance r fromthe center as J=J0rk (k is k hat) where J0 is a positive constant. Calculate the magnetic field at point P (r = 2R) from the centre,(magnitude and direction). Sketch the Amperian loop.function of r for each region below, in terms of a, b, and any physical page, uniformly distributed along its surface. Find the magnetic field as a through its cross-section, and the shell carries a total current /, into the thick wire carries a total current 1 out of the page, uniformly distributed thin cylindrical shell of radius b. (Neglect the thickness of the shell.) The A long, thick cylindrical wire of radius a is surrounded by a long. B6. 1. or numerical constants, and circle its direction. (a) B(a b) outside the shell Circle the direction: (clockwise ) (counter-clockwise ) (another direction) (there is no field)
- An electron and a proton, both with the same initial velocity, v, enter a region with a uniform magnetic field B out of the page, as shown. Each one undergoes semi-circular motion in the field and exits the field some distance d from the entry point. (The diagram shows the path for just one of the two particles.) Consider the following two statements and decide if they are true or false. i) The particle shown in the picture must be the negative one (the electron). ii) The distance "d" for the proton will be greater than "d " for the electron. В d. (shot with same v) i is true, but ii is false Both i and ii are false i is false, but ii is true Both i and ii are trueA particle of charge q moves in a circle of radius a at constant angular velocity w. (Assume that the circle lies in the xy plane, centered at the origin, and at time t=0 the charge is at (a,0), on the positive x axis.) a) Find the electric and magnetic fields at the center. b) From your formula for B you obtained in a), determine the magnetic field at the center of a circular loop carrying a steady current I.There are three parallel wires perpendicular to the paper, each carry ing current I that are located at the vertices of a right triangle. The current is coming out of the paper for wires 1 and 2 and into the paper for wire 3. Point A is at the midpoint of the hypotenuse. d 45⁰ 2 A 45° d (X) 3 Calculate the net magnetic field vector (both magnitude and direction) at A.
- PLEASE be clear in your answer since the last time I posted was incorrect, thanks.Consider a current-carrying wire of length L carrying a current of magnitude I from left to right. What is the magnetic field contribution dB⃗ at point P, with coordinates (x,y), due to the current element dl→ at point A, with coordinates (a,0)? Assume that y is positive.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?