Suppose you have a 5nC charge T the origin and a 2nC charge at x=5m. Find the location on the x axis where the electric field is 0. (Find finite coordinate location)

Question

Suppose you have a 5nC charge T the origin and a 2nC charge at x=5m. Find the location on the x axis where the electric field is 0. (Find finite coordinate location)

Answer 1

To find the location on the x-axis where the electric field is zero, we can make use of the principle of superposition and the formula for the electric field due to a point charge.

The electric field due to a point charge q at a distance r from it is given by the equation:

E = k * (q / r^2)

Where:
E is the electric field
k is the Coulomb's constant (approximately equal to 9 × 10^9 N*m^2/C^2)
q is the charge
r is the distance

In this case, we have two charges:

Charge T = 5nC at the origin (x = 0)
Charge Q = 2nC at x = 5m

Let's assume that the electric field due to Charge T cancels the electric field due to Charge Q at a certain point on the x-axis, which we need to find.

At the point where the electric field is zero, the electric fields due to both charges will have equal magnitudes and opposite directions.

So, we can set up the equation as follows:

k * (T / r^2) = k * (Q / (5-r)^2)

Notice that since the electric field is proportional to the charge, we don't need the actual values of T and Q. We just need their ratio.

Simplifying the equation, we have:

(T / r^2) = (Q / (5-r)^2)

Multiplying both sides by r^2 and (5-r)^2, we get:

T * (5-r)^2 = Q * r^2

Expanding the equation:

25T - 10Tr + Tr^2 = Qr^2

Now, we can solve this quadratic equation to find the value of r, which represents the desired position on the x-axis.

25T - 10Tr + Tr^2 - Qr^2 = 0

Since the values of T and Q are not provided, we cannot solve for the exact value of r. However, we can still find the general approach to finding the location where the electric field is zero by rearranging the equation:

Tr^2 - 10Tr + 25T - Qr^2 = 0

To solve this quadratic equation, you can use various techniques such as factoring, completing the square, or using the quadratic formula. Once you find the values of T and Q, substitute them into the equation and solve for r to determine the location on the x-axis where the electric field is zero.