Question

1)

three point charges are arranged as follows Q1=+q is located at (-a,0);Q2=+q is at (a,0)

Q3=-q (0,a)

a)Calculate the electric field at the origin and the point (0,-a)

b)there are two points in the field around the charges where the field around the charges where the field strength is zero.Approximately where will they be located?Sketch a vector diagram of the three field vectors at these points and show they add to zero.

2)

q1=+q is located at the origin .q2=-4q is located at x=a, y=0

(a) calculate the coordinates of a point in the field where E=0(not at infinity)

Answer 1

Answer 2

1. To calculate the electric field at the origin (0,0) and the point (0,-a), we can use the principle of superposition. The electric field at a point due to multiple point charges is the vector sum of the individual electric fields at that point.

a) Electric field at the origin (0,0):

The distance from Q1 to the origin is "a" units, and the distance from Q2 to the origin is also "a" units. The electric field due to Q1 and Q2 at the origin will have equal magnitudes but opposite directions. Since the charges are positive, the electric fields will point away from Q1 and Q2.

The magnitude of the electric field due to a point charge is given by: E = k * |q| / r^2

where: k is Coulomb's constant (approximately 8.99 x 10^9 N m^2/C^2) |q| is the magnitude of the charge (in this case, q) r is the distance from the charge to the point of interest

Thus, the electric field due to Q1 at the origin: E1 = k * |q| / a^2

The electric field due to Q2 at the origin: E2 = k * |q| / a^2

Since the electric fields are in opposite directions, their vector sum is: E_total_at_origin = E1 - E2

b) Electric field at the point (0, -a):

The distance from Q1 to the point (0, -a) is also "a" units, and the distance from Q3 to the point (0, -a) is "2a" units (using the Pythagorean theorem). The electric fields due to Q1 and Q3 at this point will have magnitudes E1 = k * |q| / a^2 and E3 = k * |q| / (2a)^2, respectively.

The electric field due to Q1 at (0, -a): E1 = k * |q| / a^2

The electric field due to Q3 at (0, -a): E3 = k * |q| / (2a)^2

Since the electric fields are in the same direction (both away from Q1 and Q3), their vector sum is: E_total_at_point(-a) = E1 + E3

2. To find the two points in the field where the field strength is zero, we need to set the total electric field (E_total) at each point to zero. Let's consider the coordinates (x, y) for the two points.

(a) Electric field at a point where E = 0:

At this point, the total electric field is zero, which means the vector sum of the electric fields due to Q1 and Q2 is zero.

The electric field due to Q1 at the point (x, y): E1 = k * |q| / ((x)^2 + (y)^2)

The electric field due to Q2 at the point (x, y): E2 = k * |(-4q)| / ((x-a)^2 + y^2)

Since the total electric field is zero, we have: E_total = E1 + E2 = 0

We can solve this equation to find the specific values of "x" and "y" at the points where the electric field is zero. Note that these points will not be at infinity, but rather at finite distances from the charges. The coordinates (x, y) will depend on the values of "a" and "q" given in the problem.

Unfortunately, without specific values for "a" and "q," we cannot provide exact numerical coordinates for the points where the electric field is zero. You can use a mathematical solver or software to find the exact coordinates based on the values of "a" and "q" you have.