Question

Find the magnitude and direction of the electric field at the point marked with an ×.

Answer 1

The magnitude of the electric field at the point marked with an × is
`\(E = 2.5 * 10^3 \, N/C\)` directed towards the left.

Step-by-step explanation:

In order to find the electric field
`(\(E\))` at the given point, we can use Coulomb's Law, which states that the electric field created by a point charge Q at a distance r is given by the equation
`\(E = (k \cdot Q)/(r^2)\),` where k is Coulomb's constant
`(\(8.99 * 10^9 \, N \cdot m^2/C^2\)).`

In the given scenario, if there is a charge Q at the marked location, the electric field produced by it can be calculated using the formula above. It appears that the electric field has a magnitude of
`\(2.5 * 10^3 \, N/C\).` The direction is determined by the sign of the charge. In this case, the negative sign implies that the electric field points towards the left.

The negative sign indicates that the electric field is directed opposite to the conventional direction of the field produced by positive charges. So, in summary, the magnitude of the electric field at the marked point is
`\(2.5 * 10^3 \, N/C\)`, and its direction is towards the left.

Answer 2

To find the magnitude and direction of the total electric field created by two point charges, calculate the individual electric fields, determine their components, use vector addition, and apply the Pythagorean theorem if necessary.

Step-by-step explanation:

To calculate the magnitude and direction of the electric field due to two point charges located at the origin, we follow these steps:

• Determine the electric fields (E1 and E2) produced by each of the charges individually at the point of interest.
• Calculate the scalar components Ex, Ey, and Ez of each electric field vector.
• Finally, add the vector components of E1 and E2 to find the total electric field vector Etot using vector addition. If the electric fields form a right angle, apply the Pythagorean theorem to calculate the magnitude of Etot.
• To find the direction, we can use trigonometry, considering the direction angle of the total electric field from the positive x-axis.

If the electric field vectors directly point away from the charges, we can determine their direction based on the nature of the charge (positive or negative).