A charged particle is connected to a string that is is tied to the pivot point P

Question

A charged particle is connected to a string that is is tied to the pivot point P. The particle, string, and pivot point all lie on a horizontal table (consequently the figure below is viewed from above the table). The particle is initially released from rest when the string makes an angle 35 degree with a uniform electric field in the horizontal plane (shown in the figure). Determine the speed of the particle when the string is parallel to the electric field. Answer in units of m/s. A charged particle is connected to a string that is is tied to the pivot point P. The particle, string, and pivot point all lie on a horizontal table (consequently the figure below is viewed from above the table). The particle is initially released from rest when the string makes an angle 35 degree with a uniform electric field in the horizontal plane (shown in the figure). Determine the speed of the particle when the string is parallel to the electric field. Answer in units of m/s.

Explanation / Answer

The length of the string is l = 2.3 m The charge on the particle attached to the string is q = 3 uC = 3 * 10^-6 C The mass of the charged particle is m = 0.014 kg The angle made by the charged particle with respect to the uniform electric field is A = 35o = 35 * (pi/180) radians = 0.610 radians The magnitude of the uniform electric field is E = 266 V/m Let the speed of the particle when the string is parallel to the field be v The force acting on the charge particle is F = E * q or m * a = E * q or a = (E * q/m) where a is the acceleration of the particle We know that a = at where at is the tangential acceleration or at = l * z where z is the angular acceleration or z = (at/l) We know from the relation w^2 - wo^2 = 2zA where wo = 0 or w^2 = 2zA or w = (2zA)^1/2 or (v/l) = (2zA)^1/2 or v = l * (2zA)^1/2

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