# Electric Field and a Charged Cork Ball on a Massless String

• gsquare567
In summary, in this problem a charged cork ball of mass 1g is suspended on a light string in the presence of a uniform electric field. When the electric field is (3i + 5j) * 10^5 N/C, the ball is in equilibrium at an angle of 37 degrees. To find the charge on the ball and the tension on the string, we can use the cosine law with the forces to isolate for the angle theta. In the equilibrium position, the tension on the string is equal to mg*cos(theta) and the electric force on the cork ball is q*E. By equating the components of these forces, we can solve for the tension and the charge on the ball.
gsquare567

## Homework Statement

A charged cork ball of mass 1g is suspended on a light string in the presence of a uniform electric field. When E = (3i + 5j) * 10^5 N/C, the ball is in equilibrium at $$\theta$$ = 37 degrees. Find the charge on the ball and the tension on the string.

====================
|\
|$$\theta$$\
| \
| \ / <- uniform electric field, E = (3i + 5j) * 10^5 N/C
| \/
| O <- charged cork ball, mass = 1g, q = ?

i
^
|
|
-------> j

F(electric) = qE
F(grav) = mg(-j)

## The Attempt at a Solution

I tried using the cosine law with the forces to isolate for $$\theta$$
a^2 = b^2 + c^2 -2bc * cos($$\alpha$$)
but it canceled out.
Anyways,
$$\alpha$$ = $$\theta$$
a = F(elec)
b = F(grav)
c = F(res) = F(elec) + F(grav)

Any ideas? Thanks!

In the equilibrium position, resolve mg into two components.
mg*cosθ will provide the tension and mg*sinθ will try to bring the string into vertical position.

The magnitude of the electric field is sqrt(34) and makes an angle α = arctan(5/3)
The electric force on the cork ball is q*E.
In the equilibrium position angle between the string and the electric force is (90 +α - θ )
Its component along the string is Fe*cos(90 +α - θ) and perpendicular to the string is Fe*sin(90 +α - θ ).
Equate them with the components of mg and solve for T and q.

## 1. What is an electric field?

An electric field is a physical quantity that describes the influence of electric forces on a charged object. It is represented by a vector that indicates the direction and strength of the force that a charged object would experience at any given point in space.

## 2. How is an electric field created?

An electric field is created by a source charge, such as an electron or a proton. The source charge exerts a force on other charges in its vicinity, creating an electric field around it.

## 3. What is the relationship between electric field and charged objects?

The electric field exerts a force on charged objects within its range, causing them to experience either an attractive or repulsive force depending on their charge. The strength of the force is directly proportional to the magnitude of the electric field.

## 4. How does a charged cork ball on a massless string behave in an electric field?

A charged cork ball on a massless string will experience a force in the direction of the electric field. If the electric field is strong enough, the cork ball may also experience a torque, causing it to rotate.

## 5. What factors affect the behavior of a charged cork ball on a massless string in an electric field?

The behavior of a charged cork ball on a massless string is affected by the strength and direction of the electric field, as well as the magnitude and sign of the charge on the ball. The length of the string also plays a role in determining the motion of the cork ball.

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