Electric Field From Multiple Charges

Question

The next two questions refer to the following situation: You are given four charges: q₁ = –Q, q₂ = –4Q, q₄ = +9Q, q₅ = +3Q, and a fifth unknown charge q₃. The net E-field due to q1, q3, q4, and q5 at the location of q2 is shown and directed down and to the left at a 45 degree angle, as shown.

What is the magnitude of the E-field due ONLY to q₄ and q₅ at the location of q₂? Note that this is only a component of the net E-field due to q₁, q₃, q₄ and q₅ at the location of q₂.

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Group of answer choices

Option 5: 5kQ/r^2

Option 4: 4kQ/r^2

Option 3: 3kQ/r^2

Option 2: 2kQ/r^2

Option 1: kQ/r^2

What is the charge of q₃?

Group of answer choices

-4Q

-2Q

-12Q

+4Q

+2Q

+12Q

Answer 1

What is the magnitude of the E-field due ONLY to q₄ and q₅ at the location of q₂?

The trick to realize here is that q4 and q5 are aligned veritcally with q2. This means that their force on q2 is responsible ONLY for the vertical component of the electric field at the location of q2. Using this information, you can write an equation for the net force on q2 in the vertical direction. You would have one term for the force on q2 due to q4 and one term for the force on q2 due to q5. These terms would add up to equal the net force on q2.

What is the charge of q₃?

Similar to the previous question, we can exploit the fact that q1 and q3 are horizontally aligned with q2, and write an equation for the horizontal component of the net force on q2 as the sum of the force on q2 due to q1 and the force on q2 due to q3. This equation will have one unknown quantity (the charge of q3), which you can solve for.