Consider an electric field that is constant in magnitude and direction and point
ID: 1407553 • Letter: C
Question
Consider an electric field that is constant in magnitude and direction and points to the right, as in the picture below. A pith ball of charge q = 6x10-4 C and mass m = 0.10 kg is hung from an insulating string and is placed in the electric field. It hangs as shown in the diagram below. The magnitude of the electric field is 1000 N/C.
Calculate:
a) The gravitational force on the pith ball. Show your work.
b) The electric force on the pith ball. Show your work.
c) The tension in the string. Show your work.
d) The angle at which the pith ball hangs. Show your work.
e) If the string were cut, calculate the magnitude and direction of the initial acceleration of the ball. Show your work.
Explanation / Answer
given,
q = 6x10-4 C
m = 0.10 kg
electric field = 1000 N/C
gravitational force = mg
gravitational force = 0.1 * 9.8
gravitational force = 0.98 N
electric force = charge * electric field
electric force = 6 * 10^-4 * 1000
electric force = 0.6 N
since the ball is in equilibrium so
sum of horizontal forces = 0
electric force - T * sin(theta) = 0
electric force = T * sin(theta)
0.6 = T * sin(theta)
sum of vertical forces = 0
mg = T * cos(theta)
0.98 = T * cos(theta)
on solvng we'll get
T = 1.149 N
tension in the string = 1.149 N
theta = cos^-1(0.98 / 1.149)
angle at which the ball is hanging = 31.47 degree