Question

Using appropriate technology, you determine that Earth's magnetic field at your location has a magnitude of 5.88 10-5 T and is directed north at an angle of 56° below the horizontal. You charge a metallic projectile and fire it north with a speed of 663 m/s and at an angle of 14° above the horizontal. Determine the sign (+ or −) and charge of the projectile, if the magnetic force on the projectile is 3.22 10-10 N, directed due west.

C

Answer 1

To determine the sign and charge of the projectile, use the equation for magnetic force. The charge of the projectile is approximately -1.14 x 10-6 C, indicating a negative charge.

Step-by-step explanation:

To determine the sign (+ or -) and charge of the projectile, we need to analyze the given information and use the equations of magnetic force. The force on the projectile is given as 3.22 x 10-10 N, directed due west.

Using the formula F = qvBsin(theta), where F is the force, q is the charge, v is the velocity, B is the magnetic field, and theta is the angle between the velocity and magnetic field, we can solve for q.

Since the force is directed due west, and the projectile is fired north, the angle between the velocity and the force is 90 degrees. Therefore, sin(theta) = 1.

Plugging the given values into the equation, we have:

3.22 x 10-10 = q(663)(5.88 x 10-5)(1)

Simplifying the equation, we find that the charge of the projectile is approximately -1.14 x 10-6 C. The negative sign indicates that the projectile has a negative charge.