Find the force on the proton and its acceleration - find

Question

1. A wire carrying current I = 20.0 A has a configuration shown below. Two semi-infinite wires straight sections, each tangent to the same circle , are connected by a circular arc of radius R = 10 cm. The arc subtends an angle 0 at the center. What is the value of 0 if the magnetic field at the center is 1.2 x 10^-4 T into the page.

2. A proton with charge q_p = 1.6 x 10^-19 C and a mass Mp is accelerated through a potential difference V. The proton then enters a region of constant magnetic field B; the field is oriented perpendicular to the path of the proton. In this region, the proton's path is circular with radius Rp. Another particle with charge qx = 3qp and mass Mx follows the same conditions as the proton. The radius of its circular path is Rx which is 1.4 times as large as Rp. What is the ratio of Mx to Mp. Show details of your work.

3. A pair of point charges q₁ = +8μC and q₂ = -5.0 μC are moving as shown below with speeds V₁= 9.0 x 10⁴ m/s and v₂ = 6.50 x 10⁴ m/s. When the charges are the locations shown in the figure, what are the magnitude and direction of the magnetic field produced at the origin by the charges.

(b) Find the magnetic field at (0.4, 0) due to qi and then find the net force charge q₂ experiences.

5. A velocity selector with crossed E and B fields is to be used to select alpha particle of energy 2 x 10³ eV from a beam containing alpha particles of several energies. The magnitude of the electric field E is 1 x 10⁶ V/m. What is the magnitude of the magnetic field. The charge of an alpha particle is +2e (e = 1.6 x 10^-19C) and its mass is 4 u (lu = 1.67 x 10^-27 kg)

6. A current-carrying wire is bent into a closed semicircular loop of radius R that lies in the XY plane. This is shown below. The wire is in a uniform magnetic field that points into the page of the paper. The net force on a closed loop carrying current in a uniform magnetic field is zero.

(a) Verify that the force acting on the loop is zero

(b) Is the loop at equilibrium?

(c) Find the torque.

7. A uniform magnetic field B = 0.5 T is directed along/parallel to the x-axis. A proton with q = 1.6 x 10^-19 C and mass m = 1.67 x 10-27 kg enters the uniform magnetic field with a speed of 3.0 x 105 m/s at an angle of 600 with the x-axis.

(a) At t = 0, find the force on the proton and its acceleration

(b) Find the radius and the pitch of the resulting helical path.