(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 N$/$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.

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.

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.

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.

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