Question

ELECTRIC CHARGE AND ELECTRIC FIELD
7. Figure shows three particles with charges qı = + 2,
92 = - 2Q, and 93 - 4Q, each at a distance d from the
origin. What net electric field is produced at the origin ?
у
91
92
d
30°C
30°
х
30°
d
Find the net field
at this empty point
93​

Answer 1

Answer:

it is correct

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Answer 2

Answer:

The net electric field at the origin is:

E = sqrt(Ex^2 + Ey^2) = k * sqrt(Q^2 + 9Q^2) / d^2 = k * sqrt(10) * Q / d^2

The net electric field at the empty point is zero, since the electric fields produced by the charges cancel each other out.

Explanation:

To find the net electric field produced at the origin due to the three particles with charges q1 = +2Q, q2 = -2Q, and q3 = -4Q at a distance d from the origin, we can use the principle of superposition.

First, we need to find the electric field produced by each individual charge at the origin. The electric field produced by a point charge q at a distance r from the charge is given by Coulomb's law:

E = k * q / r^2

where k is the Coulomb constant. Since the distance of all three charges from the origin is d, the electric field produced by each charge at the origin is:

E1 = k * 2Q / d^2 (directed along the positive x-axis)

E2 = k * (-2Q) / d^2 (directed along the negative y-axis)

E3 = k * (-4Q) / d^2 (directed along the negative x-axis)

To find the net electric field at the origin, we need to add the electric fields produced by each charge vectorially. The x-component of the net electric field is the sum of the x-components of the individual electric fields, and the y-component of the net electric field is the sum of the y-components of the individual electric fields.

The x-component of the net electric field is:

Ex = E1 * cos(30°) + E3 * cos(30°) = k * Q / d^2

where we have used the fact that the x-component of E1 is equal to the x-component of E3, and both are directed along the negative x-axis.

The y-component of the net electric field is:

Ey = E2 + E1 * sin(30°) = -k * 3Q / d^2

where we have used the fact that the y-component of E1 is equal to E3 * sin(30°), which is negligible compared to E2.

Therefore, the net electric field at the origin is:

E = sqrt(Ex^2 + Ey^2) = k * sqrt(Q^2 + 9Q^2) / d^2 = k * sqrt(10) * Q / d^2

where we have used the Pythagorean theorem to find the magnitude of the net electric field. The direction of the net electric field is given by the angle θ such that tan(θ) = Ey / Ex.

To find the electric field at the empty point, we need to find the net electric field produced by the three charges at that point. Since the point is equidistant from all three charges, the electric field produced by each charge has equal magnitude and is directed radially outward from the charge. Therefore, the net electric field at the empty point is zero, since the electric fields produced by the charges cancel each other out.

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