(a) What must the charge (sign and magnitude) of a 1.45 g particle be for it to remain balanced

step 1 To solve this question, let's draw the free border diagram of the particle. The weight of the pa

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

(a) What must the charge (sign and magnitude) of a $1.45 \mathrm{~g}$ particle be for it to remain balanced against gravity 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 it exerts on a proton is equal in magnitude to the proton's weight?

Key Concepts

Electric Force

The electric force is the force exerted on a charged particle when it is placed in an electric field. It is given by the equation F = qE, where q is the charge of the particle and E is the magnitude of the electric field. This concept is central to understanding how electrically charged objects interact with electric fields.

Gravitational Force

Gravitational force, often referred to as weight, is the force exerted on an object due to gravity. It is calculated using the formula F = mg, where m is the mass of the object and g is the acceleration due to gravity. This force acts downward and is a key factor in problems involving balancing or counteracting other forces.

Equilibrium Condition

The equilibrium condition occurs when the net force acting on an object is zero, meaning all forces balance each other. In scenarios where a charged particle is held stationary in an electric field, the electric force must exactly counterbalance the gravitational force.

Sign Conventions in Electric Fields

Sign conventions in electric fields dictate that the direction of the force on a charged particle depends on the sign of its charge. A positive charge experiences a force in the direction of the electric field, while a negative charge experiences a force in the opposite direction. This is crucial when determining the necessary charge polarity to achieve equilibrium in the presence of a directional electric field.

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