# Charge Distributions#

Two thin rings of radius \(R\) and charges \(Q_1 = Q\) and \(Q_2 = -Q\) are centred along the \(x\)-axis as shown in the figure below.

## Part 1#

Write an expression in terms of \(x\), \(d\) and \(R\) for the distance, \(r_1\), for the distance of any point on ring 1 from point \(P\). Note that this is a right-angled triangle so you can use the pythagorean theorem.

Use the following table as a reference for each variable:

For |
Use |
---|---|

\(R\) |
R |

\(d\) |
d |

\(x\) |
x |

\(k\) |
k |

\(Q\) |
Q |

**If the answer is 0, enter “zero”**.

### Answer Section#

### pl-submission-panel#

## Part 2#

Write an expression for the electric potential at point \(P\) due to the two thin rings in terms of \(Q\), \(R\), \(d\) and \(x\).

Use the following table as a reference for each variable:

For |
Use |
---|---|

\(R\) |
R |

\(d\) |
d |

\(x\) |
x |

\(k\) |
k |

\(Q\) |
Q |

**If the answer is 0, enter “zero”**.

### Answer Section#

### pl-submission-panel#

## Part 3#

From your expression for the potential energy find the electric field at point \(P\). Note that it points along the \(x\)-axis, and remember to use the chain rule.

Use the following table as a reference for each variable:

For |
Use |
---|---|

\(R\) |
R |

\(d\) |
d |

\(x\) |
x |

\(k\) |
k |

\(Q\) |
Q |

**If the answer is 0, enter “zero”**.

### Answer Section#

### pl-submission-panel#

## Part 4#

When \(x = -\frac{d}{2}\) evaluate the electric potential.

Use the following table as a reference for each variable:

For |
Use |
---|---|

\(R\) |
R |

\(d\) |
d |

\(x\) |
x |

\(k\) |
k |

\(Q\) |
Q |

**If the answer is 0, enter “zero”**.

### Answer Section#

### pl-submission-panel#

## Part 5#

When \(x = -\frac{d}{2}\) evaluate the electric field.

Use the following table as a reference for each variable:

For |
Use |
---|---|

\(R\) |
R |

\(d\) |
d |

\(x\) |
x |

\(k\) |
k |

\(Q\) |
Q |

**If the answer is 0, enter “zero”.**

### Answer Section#

### pl-submission-panel#

## Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.