Parallel plate conductors of opposing charge and unequal magnitude

[JJK1503]

A question has occurred to me during preparation for a Physics exam. My textbook does a good job of discussing a capacitor charged equal but opposite. But I want to take it a step further. My question is how to calculate the E field between 2 plates of opposing charge that have unequal magnitudes.

For example; if I have two plates of σ and -5σ a distance x apart, what would the E field be at x/2 ? Would the magnitude of the E field be constant for any point between the plates, as it is with a capacitor? Is this a simple superposition problem where I should create a Gaussian cylinder and find E field for both adding them together or is it something else? I am definitely over thinking this one.

I feel like this is exactly the type of curve ball my professor might throw at us on Monday. Any help is much appreciated. I have spent too much time thinking about this.

 

[Tanya Sharma]

A question has occurred to me during preparation for a Physics exam. My textbook does a good job of discussing a capacitor charged equal but opposite. But I want to take it a step further. My question is how to calculate the E field between 2 plates of opposing charge that have unequal magnitudes.

For example; if I have two plates of σ and -5σ a distance x apart, what would the E field be at x/2 ? Would the magnitude of the E field be constant for any point between the plates, as it is with a capacitor? Is this a simple superposition problem where I should create a Gaussian cylinder and find E field for both adding them together or is it something else? I am definitely over thinking this one.

Welcome to PF !

Assuming you are talking about a parallel plate capacitor ,the charges on the inner surfaces of the two plates would be equal and opposite .This in turn means that there would be charges on the outer surfaces of the two plates .

Regarding the magnitude of the charges on the inner surfaces and on the outer surfaces , you need to use the condition that electric field inside the conductor is zero .

 

[my2cts]

You should be able to calculate the field of a uniform planar charge density using Gauss's law.
Simply add the contributions at x/2 of two such planes with sigma and -5 sigma.