1. (3 pts) An electron is moving to the right with a velocity of 105 m/s...

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1. (3 pts) An electron is moving to the right with a velocity of 105 m/s in a region of space where there is a constant magnetic field of 5T pointing 45 degrees upward from the horizontal (see the figure below). Define a coordinate system with x pointing to the right, y pointing up, and z out of the screen. B % 45 -> V a. Find the magnitude and direction of the force on the electron the instant it enters the field. b. Find the magnitude and direction of an electric field that could be turned on in this region which would result in a total force from both fields of zero on the electron. 2. (4 pts) Define a coordinate system with x pointing to the right, y pointing up, and z out of the screen. A proton moves through space with an initial velocity component of 106 m/s in the x direction and 105 m/s in the z direction. The proton is in a region of space where there is a magnetic field of 2T in the z direction. a. Find the radius of curvature of the helical path the proton follows. b. Find the amount of time it takes the proton to do one full helical loop (that is, one full circle as projected on the x-y plane). c. When the proton completes one full circle as projected on the x-y plane, how far away from it original position will it be in the z direction? 3. (3 pts) Draw the magnetic field lines for an arrangement of two bar magnets as indicated below: | N pole S pole. | | S pole N pole. | 1. (3 pts) An electron is moving to the right with a velocity of 105 m/s in a region of space where there is a constant magnetic field of 5T pointing 45 degrees upward from the horizontal (see the figure below). Define a coordinate system with x pointing to the right, y pointing up, and z out of the screen. B % 45 -> V a. Find the magnitude and direction of the force on the electron the instant it enters the field. b. Find the magnitude and direction of an electric field that could be turned on in this region which would result in a total force from both fields of zero on the electron. 2. (4 pts) Define a coordinate system with x pointing to the right, y pointing up, and z out of the screen. A proton moves through space with an initial velocity component of 106 m/s in the x direction and 105 m/s in the z direction. The proton is in a region of space where there is a magnetic field of 2T in the z direction. a. Find the radius of curvature of the helical path the proton follows. b. Find the amount of time it takes the proton to do one full helical loop (that is, one full circle as projected on the x-y plane). c. When the proton completes one full circle as projected on the x-y plane, how far away from it original position will it be in the z direction? 3. (3 pts) Draw the magnetic field lines for an arrangement of two bar magnets as indicated below: | N pole S pole. | | S pole N pole. |