(a) What must the charge (sign and magnitude) of a 1.45 -g...

(a) What must the charge (sign and magnitude) of a 1.45 -g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 650 $\mathrm{N} / \mathrm{C} ?$ (b) What is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?

(a) What must the charge (sign and magnitude) of a 1.45 -g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 650 $\mathrm{N} / \mathrm{C} ?$ (b) What
is the magnitude of an electric field in which the electric force on a proton is equal in magnitude to its weight?

Key Concepts

Electric Field Strength for Weight Balance

This concept involves finding the magnitude of an electric field that produces an electric force equal to the weight of a particle. By equating the gravitational force (mg) to the electric force (qE), one can solve for the required electric field strength that will counteract gravity for a given particle.

Charge Sign Determination

The determination of the charge's sign is important to ensure that the direction of the electric force opposes the gravitational force. For instance, if the electric field is directed downward, a negatively charged particle will experience an upward electric force, potentially balancing its downward weight.

Electric Force

Electric force is the force experienced by a charged particle when it is placed in an electric field. This force is given by the equation F = qE, where q is the charge of the particle and E is the magnitude of the electric field. The direction of the force depends on both the direction of the field and the sign of the charge.

Gravitational Force

Gravitational force, often referred to as weight, is the force with which the Earth attracts a mass. It is calculated using the equation F = mg, where m is the mass of the object and g is the acceleration due to gravity. This force acts in the downward direction near the Earth's surface.

Equilibrium Condition

The equilibrium condition in mechanics occurs when the sum of all forces acting on an object is zero, resulting in no acceleration. For a charged particle in an electric field, achieving equilibrium requires that the electric force exactly balances the gravitational force, i.e., qE = mg.

Transcript

00:01 Oh, so in this problem, i have a point source.

00:07 We're solving for the charge.

00:11 It is, since it has mass, it's experiencing downward force due to gravity.

00:18 I'll label that fg, g for gravitational.

00:23 And there is a downward electrical field of 650 newtons per coulone.

00:32 So the question's asking, what charge does this need to be in order for this charge to have, to remain stationary and not be pulled down by gravity? and since our positive electrical field is downward, this charge must be negative in order to produce an opposite.

01:07 But equal electrical force.

01:12 That is upward and resists the gravitational force.

01:20 So in order for it to be stationary, the upward electrical force must be the opposite but equal to the gravitational force.

01:31 So and as we know about electrical forces, the electrical force is equal to the charge of a point source here, times, the electrical field that's acting upon it.

02:08 This is going to be equal to the downward gravitational force, which is the mass times our gravitational constant 9 .81 meters per second squared.

02:25 Of course we're assuming this is on earth.

02:28 If we're not on earth, then we have to use an entirely different equation.

02:37 All right, so in in order to solve for the charge, all we need to do is divide both sides by the electric field.

02:48 That leaves us with q equals negative mg over e.

03:06 So we're going to plug in our numbers here.

03:12 So we have 1 .45 times 10 to negative 3 kilograms since we're using si units.

03:36 Running out of room here times 9 .81 meters per second squared for our gravitational acceleration all over our electric field which is 650 newtons per coulome...

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