Electric Field Lines and Net Charge Determination for a Grounded Metal Sphere

[ENGRstudent00]

Homework Statement

A grounded metal sphere is placed inside an original uniform electric field. Complete the electric field lines and determine the total net charge on the metal sphere (zero/pos or neg).

The Attempt at a Solution

I was thinking the electric field lines would enter then exit the sphere perpendicular to the sphere's surface. So i thought the total net charge would then be zero.

Any help, thoughts, or guidence?

 

[Gear300]

You got the field lines being perpendicular right --- if the sphere is grounded from the left, then the charges that lean towards the left (in this, positive charges) will promote a voltage difference with the ground; so there is a good chance the sphere will be left with some charge.

 

[Andrew Mason]

Is this a hollow or a solid metal sphere?

AM

 

[ENGRstudent00]

Is this a hollow or a solid metal sphere?

AM

My understanding is that this is a hollow sphere.


I pretty sure that when an uncharged conductor is placed in an electric field, the electric field lines will look like i drew above, making the charges move left, thus making the object polarized. I just don't know/understand what effect grounding the object does to the object or the electric field lines.

Thanks!

 

[ENGRstudent00]

You got the field lines being perpendicular right --- if the sphere is grounded from the left, then the charges that lean towards the left (in this, positive charges) will promote a voltage difference with the ground; so there is a good chance the sphere will be left with some charge.

So, with the charges moving left making the object's right side positive, would the ground give the object more charges to offset the positives on the right?

 

[Gear300]

So, with the charges moving left making the object's right side positive, would the ground give the object more charges to offset the positives on the right?

Yup...the potential difference with the ground would allow electrons to move into the sphere and offset the positive charge distribution. This would leave the sphere with a negative charge distribution.