What must the charge (sign and magnitude) of a particle of mass 1.48g be for it to remain stationary when placed in a downward-directed electric field of magnitude 670N/C ?

What is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?

To find the charge of a particle that remains stationary in an electric field, you need to understand the relationship between the electric field, charge, and the force acting on the particle. The electric force experienced by a charged particle in an electric field is given by the equation:

F = q * E

Where:
F is the force on the particle,
q is the charge of the particle, and
E is the electric field.

For the first question, the particle is stationary, which means the force on it must be zero. Therefore, we can set up the equation:

0 = q * E

Substituting the given values:
0 = q * 670 N/C

To find the magnitude of the charge, we need to solve the equation for q. Since any multiple of zero is zero, the charge can be any value as long as it is zero. Hence, for the particle to remain stationary, its charge must be zero.

For the second question, we need to determine the electric field magnitude that will produce a force on a proton equal to its weight. The weight of an object is given by:

Weight = Mass * Gravitational Field Strength

The gravitational field strength near the Earth's surface is approximately 9.8 N/kg. Therefore, the weight of a proton (whose mass is approximately 1.67 x 10^-27 kg) can be calculated as:

Weight = (1.67 x 10^-27 kg) * (9.8 N/kg)

Now, we equate this weight to the electric force:

Weight = q * E

Substituting the known values:
(1.67 x 10^-27 kg) * (9.8 N/kg) = q * E

Solving for E, we get:
E = (1.67 x 10^-27 kg * 9.8 N/kg) / q

The magnitude of the electric field required for the electric force on a proton to be equal to its weight depends on the charge of the proton, q. As the question does not provide the charge of the proton, it is not possible to determine the exact magnitude of the electric field without this information.