AP Physics 2 Exam Question

A positively charged particle with a charge of +2 μC is placed at a point in an electric field. The electric field is directed towards the positive $x$-direction and has a magnitude of 1000 N/C. The particle experiences an electric force of 4 N in the negative $y$-direction.

a) Determine the magnitude and direction of the electric field at the point where the particle is located. b) Determine the mass of the particle if it experiences an acceleration of 2 m/s² in the negative $y$-direction when placed in the electric field.

Given: Charge of particle $(q) = +2 \mu C = +2 \times 10^{-6} C$ Electric field magnitude $(E) = 1000 N/C$ Electric force $(F) = -4 N$ Acceleration $(a) = -2 m/s^2$

a) Determining the Electric Field Magnitude and Direction

When a charged particle is placed in an electric field, the particle experiences an electric force given by the equation:

Where:

• $F$ is the electric force (in Newtons),
• $q$ is the charge of the particle (in Coulombs),
• $E$ is the electric field strength (in N/C).

From the given information, we have:

Solving for the electric field magnitude, we can rearrange the equation to:

Substituting the given values, we have:

Calculating the electric field magnitude:

The negative sign indicates that the electric field is directed opposite to the positive x-direction.

Therefore, the magnitude of the electric field at the point where the particle is located is 2,000,000 N/C and it is directed opposite to the positive x-direction.

b) Determining the Mass of the Particle

The equation for the force experienced by a particle in an electric field is given by Newton's second law:

Where:

• $F$ is the force (in Newtons),
• $m$ is the mass of the particle (in kilograms),
• $a$ is the acceleration (in m/s²).

From the given information, we have:

Solving for mass, we can rearrange the equation to:

Substituting the given values, we have:

Calculating the mass of the particle:

Therefore, the mass of the particle is 2 kg.