A particle with charge q = -1.00x10-8 C has, at a given instant, a speed v = 3.00x 104 m/s in the xy plane directed at an angle of 30 degrees clockwise from the y axis as shown below. A magnetic field of magnitude B = 1.00 T is along the y axis in the positive direction, upward on the page. The x-y axes lie in the plane of the page. The z-axis is perpendicular to the page and the positive z-direction is out of the page.

A proton enters a uniform magnetic field of 1.0 × 10−4 T with a speed of 5 × 105 m/s. At what angle must the magnetic field be from the velocity so that the pitch of the resulting helical motion is equal to the radius of the helix?

AS0.0-g metal ball having net charge Q = 5.50 µC is thrown out of a window horizontally north at a speed v = 22.0 m/s. The window is at a height h = 18.0 m above the ground. A uniform, horizontal magnetic field of magnitude B = 0.0100 T is perpendicular to the plane of the ball's trajectory and directed toward the west. (a) Assuming the ball follows the same trajectory as it would in the absence of the magnetic field, find the magnetic force acting on the ball just before it hits the ground. (Let the +x-direction be toward the north, the +y-direction be up and the +z-direction be east.) B. (b) Based on the result of part (a), is it justified for three-significant-digit precision to assume the trajectory is unaffected by the magnetic fleld? O Yes O No Explain.

As shown in the figure, a small particle of charge q= 6.3 µ C and mass 3.84 x 1012 kg has velocity 9.0 x 10° m/s as it enters a region of uniform magnetic field. The particle is observed to travel in the semicircular path shown, with radius R= 5.0 cm. Calculate the magnitude and direction of the magnetic field in the region in T. If the field is into the page, give a negative number. If the field is out of the page, give a positive number. Region of magnetic field R Path of the particle