A point charge on a string in equilibrium with electric field

AI Thread Summary
A user is struggling to determine the magnitude and sign of a point charge in equilibrium with a uniform electric field, having calculated a charge of 6.5 x 10^-7 C instead of the expected 7.8 x 10^-7 C. They derived the angle of the pendulum using trigonometric functions based on the height and length of the string. Despite following the correct equations, they are unsure of their error. Other participants suggest that the discrepancy may stem from a potential error in the provided answer from the textbook. The discussion highlights the possibility of incorrect textbook solutions in physics problems.
saw176
Messages
14
Reaction score
0
Hi everyone, I took a look at previous questions similar to this one and it seems like I am doing everything correctly, but I still get the wrong answer. Any advice to where I am going wrong would be greatly appreciated!

Homework Statement


A point charge (m=1.0g) at the end of an insulating string of length 55 cm is in equilibrium in a uniform horizontal electric field of 12,000 N/C (which points to the right, in the direction of the pendulum's "swing"), when the pendulum's position is with the charge 12 cm above the lowest vertical position. Determine the magnitude and sign of the point charge.

Homework Equations


Tcos(theta) = mg
Tsin(theta) = qE

The Attempt at a Solution


First I found the angle theta by subtracting the height, 12 cm, from the length of the pendulum string, 55 cm. So the height is 43 cm, and applying cos(theta) = 43/55 I found the angle to be 38.6 degrees.

Next, I took the above sin and cos equations and put sin over cos to get:
tan (theta) = qE / mg
tan (38.6) = q (12,000) / (0.001)(9.80)

Solving for q, I keep getting 6.5 x 10-7 C, but the correct answer is 7.8 x 10-7 C. What am I doing wrong? Thanks for your help!
 
Physics news on Phys.org
I do not see anything wrong in your work. Your result looks right.
The given answer can be wrong. It happens.

ehild
 
Thanks ehild! I actually saw somewhere online else a student saying they got that same answer and wondering where they went wrong, so you just might be right that the book is incorrect!
 
It happens quite often.

ehild
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top