Question

in a 1.27 t magnetic field directed vertically upward, a particle having a charge of magnitude 8.40 μc and initially moving northward at 4.70 km/s is deflected toward the east.A. what is the sign of the charge of this particle? (Question asks for a sketch but an explanation would be fine)B. Find the magnetic force on the particle.

Answer 1

The charge of the particle is positive and the magnetic force is 5.36 x 10⁻² N.

Step-by-step explanation:

To determine the sign of the charge of the particle, we need to look at the direction in which the particle is deflected. The particle is moving northward and is deflected toward the east. According to the right hand rule, if the force is perpendicular to both the magnetic field and the velocity of the particle, the sign of the charge is positive. Therefore, the charge of the particle is positive.

To find the magnetic force on the particle, we can use the equation F = qvBsinθ, where F is the force, q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field. In this case:

q = 8.40 μC = 8.40 x 10⁻⁶ C

v = 4.70 km/s = 4.70 x 10³ m/s

B = 1.27 T

θ is 90 degrees since the particle is moving perpendicular to the magnetic field.

Substituting these values into the equation, we have:

F = (8.40 x 10⁻⁶ C)(4.70 x 10³ m/s)(1.27 T)(sin 90°) = 5.36 x 10 N

So, the magnetic force on the particle is 5.36 x 10⁻² N.

Answer 2

The particle is positively charged based on the direction of deflection and the right-hand rule. The magnetic force on the particle is 4.00 x 10^-2 N.

Step-by-step explanation:

To determine the sign of the charge of a particle deflected in a magnetic field, one needs to consider the direction of the magnetic field and the direction of the deflection in relation to the initial velocity of the particle according to the right-hand rule. For a magnetic field directed vertically upward and a particle initially moving north that is deflected toward the east, the force must be toward the east. According to the right-hand rule, this indicates that a positively charged particle would experience a force in that direction given the initial northward motion.

To calculate the magnetic force on the particle, use the equation F = qvB sin(θ), where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field. In this case with the velocity perpendicular to the magnetic field, sin(θ) becomes 1, so the force is simply the product of the charge, velocity, and magnetic field strength.

Force = Charge (q) * Velocity (v) * Magnetic Field (B)
Force = 8.40 × 10-6 C * 4.70 × 103 m/s * 1.27 T = 4.00 × 10-2 N