A small plastic ball of mass m=2.00 g is suspended by a string of length L=20.0 cm in a uniform

step 1 So here in this problem we have to calculate the net charge on the ball and we are given that th

A small plastic ball of mass m=2.00 g is suspended by a...

A small plastic ball of mass $m=2.00 \mathrm{g}$ is suspended by a string of length $L=20.0 \mathrm{cm}$ in a uniform electric field, as shown in Figure $\mathrm{P} 15.52$ . If the ball is in equilibrium when the string makes a $\theta=15.0^{\circ}$ angle with the vertical as indicated, what is the net charge on the ball?

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Key Concepts

Static Equilibrium

This principle states that an object remains at rest when the net force acting on it is zero. In problems like this one, the forces acting on the object (gravitational, electric, and tension) must balance out such that both the horizontal and vertical components sum to zero.

Vector Decomposition

Decomposing forces into their horizontal and vertical components allows the analysis of each directional effect separately. This is particularly useful in equilibrium problems where forces at angles, such as tension, must be split into perpendicular components to match other forces like gravitational and electric forces.

Gravitational Force

This is the force acting on a mass due to gravity and is calculated as mg, where m is the mass and g is the acceleration due to gravity. It acts vertically downward and is counterbalanced by other forces in equilibrium scenarios.

Electric Force

The electric force on a charged object in an electric field is determined by the product of the net charge and the magnetic field strength (qE). This force acts in the direction of the field (or opposite if the charge is negative) and is critical in analyzing equilibrium when electric fields are present.

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