Problem 32.

You want to create an electric field at location . Where would you place a proton to produce this filed at the origin? Instead of a proton, where would you place an electron to produce this filed at the origin?

Solution

We have only y-component of electric field. It means that the charge should be placed along axis y. Since the y-component of electric field is positive and the proton is positively charge particle then the coordinate of the proton should be negative. The magnitude of electric field is

Where y is the coordinate of the proton. Then from this equation we can find y and we remember that y is negative:

Since the charge of an electron is negative then the coordinate of electron should be positive (to produce the positive y-coordinate of electric field. The magnitude of the electron charge is the same as the magnitude of the proton charge. Then the position of electron is