A small charged ball is suspended between two large, parallel, and vertical metal plates. The electric field between the plates is uniform and horizontal. If the charge on the ball... A small charged ball is suspended between two large, parallel, and vertical metal plates. The electric field between the plates is uniform and horizontal. If the charge on the ball is doubled, how does the angle the suspension string makes with the vertical change, assuming the ball remains in equilibrium?
Understand the Problem
The question describes a charged ball suspended in an electric field between two parallel plates. The ball is in equilibrium, meaning the forces acting on it (gravity, electric force, and tension) are balanced. We need to determine how the angle of the suspension string changes when the charge on the ball is doubled, while maintaining equilibrium.
Answer
The angle increases, with tan(θ) doubling.
If the charge on the ball is doubled, the angle the suspension string makes with the vertical will increase such that tan(θ) doubles, where θ is the angle with the vertical.
Answer for screen readers
If the charge on the ball is doubled, the angle the suspension string makes with the vertical will increase such that tan(θ) doubles, where θ is the angle with the vertical.
More Information
The electric force acting on the charged ball is given by F = qE, where q is the charge and E is the electric field. The angle θ that the string makes with the vertical is determined by the balance between the electric force and the gravitational force. Specifically, tan(θ) = F/mg = qE/mg. If q is doubled, then tan(θ) doubles, meaning the angle increases, but not necessarily by a factor of two.
Tips
A common mistake is assuming the angle doubles directly when the charge doubles. The relationship is with the tangent of the angle, not the angle itself.
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