A spherical rain drop of radius 1.0 mm has a charge of +2.0 nC. The electric field in the vicini

step 1 So according to the given question, I can write the value of FD is equal to bv square. So it can

A spherical rain drop of radius 1.0 mm has a charge of +2.0...

A spherical rain drop of radius $1.0 \mathrm{mm}$ has a charge of $+2.0 \mathrm{nC}$. The electric field in the vicinity is $2.0 \mathrm{kN} / \mathrm{C}$ downward. The terminal speed of an identical but uncharged drop is $6.5 \mathrm{m} / \mathrm{s}$. The drag force is related to the drop's speed by $F_{\mathrm{d}}=b v^{2}$ (turbulent drag rather than viscous drag). Calculate the terminal speed of the charged rain drop.

Key Concepts

Force Equilibrium

Force equilibrium is the condition in which all the forces acting on an object balance out, resulting in no net force or acceleration. For a falling object like a raindrop, this equilibrium is achieved when the sum of gravitational force, electrostatic force, and drag force are perfectly balanced, leading to a constant terminal speed.

Electrostatic Force

The electrostatic force on a charged object in an electric field is given by the product of the charge and the electric field strength (F = qE). This force can act either in the direction of the field or opposite to it depending on the sign of the charge, thereby influencing the net force and the motion of the object.

Terminal Velocity

Terminal velocity is the constant speed reached by an object when the net force acting on it becomes zero. At this speed, the downward force (gravitational pull plus any additional forces such as electrostatic force) is exactly balanced by the opposing drag force, resulting in no further acceleration.

Drag Force

Drag force is the resistive force that opposes an object's motion through a fluid, often air, and in turbulent conditions it is proportional to the square of the speed. This quadratic relationship means that as the object’s velocity increases, the drag force increases significantly, eventually balancing the pulling forces acting on the object.

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