A very small charged block with a mass of 2.35 g is placed...

A very small charged block with a mass of 2.35 g is placed on an insulated, frictionless plane inclined at an angle of $17.0^{\circ}$ with respect to the horizontal. The block does not slide down the plane because of a $465-\mathrm{N} / \mathrm{C}$ uniform electric field that points parallel to the surface downward along the plane. What is the sign and magnitude of the charge on the block?

A very small charged block with a mass of 2.35 g is placed on an insulated, frictionless plane inclined at an angle of $17.0^{\circ}$ with respect to the horizontal. The block does not slide down the
plane because of a $465-\mathrm{N} / \mathrm{C}$ uniform electric field that points parallel to the surface downward along the plane. What is the sign and magnitude of the charge on the block?

Key Concepts

Static Equilibrium

This concept refers to the condition where the net force acting on an object is zero, meaning all forces balance each other perfectly, and the object remains at rest. In problems like these, setting up equilibrium conditions along the direction of potential motion allows us to relate different forces and solve for unknown quantities.

Gravitational Force Decomposition

When dealing with objects on inclined planes, gravitational force is typically broken down into components parallel and perpendicular to the plane. The parallel component, given by mg sin(?), is what tends to cause the object to slide down the incline, and understanding this decomposition is essential for analyzing motion or equilibrium on slopes.

Electric Force on a Charged Object

A charged particle in a uniform electric field experiences an electric force calculated as the product of its charge and the electric field strength (F = qE). The direction of this force depends on the sign of the charge, with positive charges being accelerated in the field direction and negative charges in the opposite direction.

Charge Sign Determination

Determining the sign of the charge involves comparing the direction of the required balancing force against the direction of the applied electric field. When the net force must oppose a specific component (such as the gravitational component on an inclined plane), knowing the electric field’s direction informs whether the charge must be positive or negative to produce a force in the opposite direction.

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