proton moves in a helical path at speed v = 5.90 × 107 m/s high above the atmosphere, where Earth’s magnetic field has magnitude B = 4.10 × 10−6 T. The proton’s velocity makes an angle of 25.0° with the magnetic field. The mass of the proton is 1.673×10−27 kg. Find the radius of the helix. ____km

3. An electron is placed with an initial velocity of 3.00 m/s east in a region of space which has either an electric or magnetic field present. For each part of this question, find the force on the electron (magnitude and direction) and describe what the effect will be on the electron’s trajectory. Will the trajectory be linear, circular, helical, or something else? Will the particle speed up, slow down, or have constant speed? Make sure to explain all answers with computations or written explanations. a. The region has an electric field of 42.0 N/C east and no magnetic field.     Force:      Shape of trajectory:      How the speed changes:  b. The region has no electric field and a magnetic field of 870 µT east.     Force:      Shape of trajectory:      How the speed changes:  c. The region has no electric field and a magnetic field of 119 µT north.     Force:      Shape of trajectory:      How the speed changes:

A science fiction author describes a space vehicle launching system consisting of a long linear track built at an angle into a mountain range on the moon. The space vehicle is mounted on a cradle that is accelerated by a magnetic field generated by the track at a constant 100. m/s². a. How fast is the vehicle going after it has traveled the 2.88 X 10^4 m track? b. How long does it take to reach this speed?

2. A proton travels with a speed of 5 x 105 m/s between the two parallel charged plates shown in the figure below. The plates are separated by 1.0 cm and charged by a 220 V battery. a. Determine the strength and direction of the electric field between the two plates. b. What is the direction and magnitude of the force on the proton due to this electric field? + + + + + + + + + + 1.0 cm c. What magnetic field (strength and direction) will allow the proton to pass between the plates without being deflected?

5. A proton zipping along with a velocity v = 3 × 105î + 4 × 105k m/s enters a region of uniform magnetic field. The magnetic field points along the z (k) direction with a strength of 0.5T. (M,=1.67x10-27 kg) a) What is the force (magnitude and direction) acting on this particle (ignore gravity)? b) What is the radius of the curved path the proton will take?

1. Two current carrying wires are situated as in the figure shown above. The wire on the left carries a current of I1 and the rectangular wire carries at current of I2. Keeping the dimensions as c, a, and l to be arbitrary, find the net force exerted on the loop by the magnetic field by the wire. (ch. 30, problem 25, physics for scientists and engineers)

The magnetic force dFg on a infinitesimal segment of current I is dFs = I dEx B Where di is the displacement vector of the infinitesimal current segment. The total magnetic force on a finite current segment is F = 1J (dL x B) 1. If the magnetic field is uniform in space the magnetic force on current simplifies to FB = {(x5). What is vector in this expression? Choose one. is the length of the current segment is the vector from the point where the current enters the uniform field to the point where the current leaves the uniform field. a. What is the magnetic force on the portions of the wire to the left of the dashed line? • is the current. 2. The magnetic field is zero to the left of the dashed line. The magnetic field to the right of the dashed line is uniform outwards. A current carrying wire goes through the region as shown. b. What is the magnetic force on the bottom wire segment? Write answer in component vector form. c. What is the magnetic force on the slanted wire segment?…

4. In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish 12C+ and 14C+ ions. The 12C+ ions move in a circle of diameter 29.3 cm. Use these atomic mass values: 12C, 12.0 u; 14C, 14.0 u. What is the diameter of the orbit of 14C+ ions? _____cm

Near the surface of the earth, a magnet is made to levitate above another magnet, which is on a table, due only to magnetic force. The levitating magnet has a mass of 150 g with its north pole facing the magnet on the table and its south pole facing upwards.   1. Sketch a free-body diagram of the levitating magnet. 2. Determine the magnetic force on the levtiating magnet. 3. Sketch the magnetic field between the two magnets. 4. A stream of electrons is shot between the magnets, perpendicular to the field. Describe, in general, what will happen to the electrons, ignoring the effects of gravity on the electrons. (Will they continue traveling straight or will their path deviate and why?)

8. This time I1 = 1.61, I2 = 4.86 A, and the two wires are separated by 8.83 cm. Now consider the charge q = 2.22 x 10^-6 C, located a distance of 4.50 cm to the right of wire I2, moving to the right at speed v = 48.4 m/s. What is the magnitude of the total magnetic force on this charge?     2.58E-09 N   1.81E-09 N   1.09E-09 N   5.45E-10 N