What charge would have to be fixed at the origin?

In summary, the question asks for the charge ##Q## that needs to be placed at the origin in order for the tension in the rope to become zero. This can be solved by setting the tension equation to 0 and solving for ##Q##, using the given values for mass, velocity, magnetic field, and rope length. However, this is not the same as the charge on the ball, which is given as 3.0C. The solution for ##Q## is 10C.
  • #1
TRVSA
4
0

Homework Statement


A ball of mass m is attached to a rope of length L which has one end at the origin; the ball moves in a horizontal circle at constant speed v0 on a frictionless plane; the velocity is always at 90◦ to the rope. The ball has a charge q, and moves in a constant magnetic field which is directed vertically B⃗ = B0kˆ. At the time illustrated, the ball is at location ⃗r = L cos θˆı + L sin θˆ, with velocity ⃗v = −v0 sin θˆı + v0 cos θˆ.

  1. Assume that q = 3.0[C], B0 = 1.0[T], v0 = 5.0[m/s], m = 4.0[kg], and L = 2.0[m], what charge would have to be fixed at the origin in order the tension in the rope became 0?

Homework Equations


T = mv0^2/L + qv0B0

The Attempt at a Solution



I set T to 0, plugged in the values given and tried to solve for q.
 
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  • #2
TRVSA said:
I set T to 0, plugged in the values given and tried to solve for q.

Please explicitly show what you did and where you got stuck.
 
  • #3
PeterDonis said:
Please explicitly show what you did and where you got stuck.

0 = (4kg)(5m/s)2/2(2.0m) + q(5m/s)(1T)
10 = q

which obviously is not the answer. that was just a shot in the dark. I know q is given as 3.0C.. I just do not know how to solve for the charge at the origin.
 
  • #4
TRVSA said:
I know q is given as 3.0C..

That's the charge on the ball. You are not being asked to solve for that. You are being asked to find what charge ##Q## (note the capital letter to show that it's a different charge we're talking about) would have to be placed at the origin for the tension in the rope to be zero. In other words, the charge ##Q##, when placed at the origin, should exert the same force on the ball as the tension in the rope does when the charge ##Q## is not there.
 

FAQ: What charge would have to be fixed at the origin?

1. What is meant by "charge fixed at the origin"?

When we say a charge is fixed at the origin, it means that a positive or negative charge is placed at a specific point in space, usually represented by the coordinates (0,0) in a Cartesian coordinate system.

2. Why would we want to fix a charge at the origin?

Fixing a charge at the origin is often done in theoretical or mathematical models to simplify calculations and understand the behavior of the electric field in a specific region of space.

3. How is the electric field affected by a fixed charge at the origin?

The electric field is affected by a fixed charge at the origin as it creates a radial electric field that extends outwards from the origin. The strength of the field decreases with distance from the origin, following the inverse square law.

4. Can a fixed charge at the origin be positive or negative?

Yes, a fixed charge at the origin can be either positive or negative. A positive charge at the origin will create an outward-pointing electric field, while a negative charge at the origin will create an inward-pointing electric field.

5. How does a fixed charge at the origin affect other charges in its vicinity?

A fixed charge at the origin can attract or repel other charges in its vicinity, depending on the sign of the charges and their distances from the origin. The force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

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