Question

A small sphere with a mass of 441 g is moving upward along the vertical +y-axis when it encounters an electric field of 5.00 N/C . If, due to this field, the sphere suddenly acquires a horizontal acceleration of 13.0 m/s2, what is the charge that it carries?

A) 1.15 C

B) -1.15 C

C) 1150 C

D) -1150 C

Answer 1

Concepts and reason

The concepts used to solve this problem are force due to the electric field, Newton’s first law of motion, and Newton's second law of motion.

First, use the concept of force due to the electric field and then Newton's second law of motion to determine the charge on the body.

Fundamentals

Force due to the electric field:

It is a force which is experienced by the body due to the electric field.

Mathematically the force due to the electric field can be represented as,

Here, the force due to the electric field is, the electric field is and the charge is.

Newton’s first law of motion:

It states that a body follows its state of rest or motion unless or until an external force is applied.

Newton's second law of motion:

It states that the rate of change of linear momentum of a body directly proportions to the applied force.

Mathematically it can be expressed as,

Here, the applied force is , the mass of the body is and acceleration of the body is.

The diagram of the problem is given as,

When the mass enters into the electric field it experiences the electric force in the direction of the electric field.

As the body is accelerating,

Here, is the force due to the electric field.

Substitute for in the above equation,

Substitute for, for and for in the above equation,

The value of the charge is.

Ans:

The charge carried by the body is.