Question

What is the minimum magnitude of an electric field that balances?

Answer 1

The minimum magnitude of an electric field that balances a charge is found using the equation F = qE, where F is the force and q is the charge. By equating F with opposing forces like gravity, one can calculate the required electric field magnitude to achieve balance.

Step-by-step explanation:

The question asked is about finding the minimum magnitude of an electric field that can balance a charged particle. To answer this, we use the formula F = qE, where F is the force, q is the charge, and E is the electric field magnitude. For a balancing scenario, the electric force would have to be equal and opposite to another force, such as gravity. Assuming we want to balance against the Earth's gravity, we would equate F with the weight of the charged particle.

For example, if we consider the case of an electron near Earth's surface, we would need to balance its weight, which is the product of its mass and the acceleration due to gravity. To find the electric field that balances this weight, we would use the formula E = F/q. By calculating, you would be left with the answer for the magnitude of the required electric field.

Answer 2

The minimum magnitude of an electric field that balances is the gravitational force acting on an object, given by the equation E = mg/q, where E is the electric field, m is the mass of the object, g is the acceleration due to gravity, and q is the charge of the object.

Step-by-step explanation:

When discussing the balance between gravitational force and the electric field, we are referring to the point where these two forces are equal, resulting in equilibrium. The force experienced by a charged object in an electric field (Fₑₗₑcₜᵢc) is given by Coulomb's Law: Fₑₗₑcₜᵢc = qE, where q is the charge of the object and E is the electric field. At equilibrium, this electric force is equal to the gravitational force acting on the object, given by Fᵢₑₗdₗₖᵢc = mg, where m is the mass of the object and g is the acceleration due to gravity.

Setting Fₑₗₑcₜᵢc equal to Fᵢₑₗdₗₖᵢc and rearranging the equation, we get qE = mg. Solving for the electric field (E), we find E = mg/q. This equation represents the minimum magnitude of the electric field required to balance the gravitational force on the object. It's important to note that this scenario is a simplified model and assumes a uniform electric field, neglecting factors like air resistance.

Understanding the interplay between electric and gravitational forces is fundamental in physics, providing insights into the behavior of charged objects in different environments and contributing to the broader understanding of electromagnetism.