Note: Mass of an electron is 9.110-31kg; Charge of an electron is 1.610-19C. 1.

Question

Note: Mass of an electron is 9.110-31kg; Charge of an electron is 1.610-19C. 1. A proton enters a region of a uniform magnetic field with velocity v = 3.0106m/s in + X direction. The magnitude of the field is 2.0 T and is in Y direction. What is the magnetic force (magnitude and direction) exerted on the proton from the field? (9.6e-13 N in Z direction) 2. An electron enters a region of a uniform magnetic field with velocity v = 3.0106m/s in + X direction. The magnitude of the field is 2.0 T and is in Y direction. What is the magnetic force (magnitude and direction) exerted on the proton from the field? (9.6e-13 N in +Z direction) 3. An electron enters a region of a uniform magnetic field with velocity v = 3.0106m/s in + X direction. The magnitude of the field is 2.0 T and is in X direction. What is the nature of electrons trajectory in this field (a line, a circle, of a helix)? (A line) 4. A proton enters a region of a uniform magnetic field with velocity that has x- and y-components, v = (3.0106m/s) x + (-2.0106m/s) y. The magnitude of the field is 2.0 T and is in - X direction. What is the nature of protons trajectory in this field (a line, a circle, of a helix)? (A helix) 5. An electron enters a region of a uniform magnetic field with velocity v = 3.0106m/s in + X direction. The magnitude of the field is 2.0 T and is in Y direction. What are the radius and direction of electrons circular orbit? (8.5?m clockwise as viewed toward +X direction)

Explanation / Answer

1. force = Bqvsin(t) = 2*1.6*10^-19*3.0*10^6 * sin(90) = 9.6*10^-13 in -z direction.

2. force = - 2*1.6*10^-19*3*10^6 * 1 =9.6*10^-13 in z direction. because charge on electron is negative.

3. since B and v are along +x and -x direction, angle between them is 180.. so net force is 0. Particle motion is uneffected. so

motion is straight line..

4. Since there is a component of velocity in x-direction and also in y direction, the charged particle still completes a revolution, but not in the circular plane because charged particle also moves in the direction perpendicular to the circular plane. The net result is that the path of revolution is a stretched out series of circles in the form of a helix.

5. Radius = mv/Bq = 9.1*10^-31*3.0*10^6/(2*1.6*10^-19) =8.53 micro m in +x direction.

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