Final answer:
To determine the distance from the first charge where the electric field is zero when two charges are present, establish an equation based on the electric fields of both charges cancelling each other out and solve for the desired distance.
Step-by-step explanation:
Finding the Zero Electric Field Point Between Two Charges
To find at what distance r from the first charge (q1) the electric field is zero when two charges, q1 = 2.2 × 10-6C and q2 = 5.2 × 10-6C, are separated by a distance of d = 1.25 m, we need to use the principle that at the point where the electric field is zero, the fields produced by the two charges will cancel each other out.
The electric field E due to a point charge q at a distance r is given by E = kq/r², where k is Coulomb's constant. To find the distance r from q1 where the electric field is zero, we set up the equation kq1/r² = kq2/(d-r)². Here r is the distance from q1 to the point where the field is zero, and (d-r) is the distance from q2 to that same point.
After canceling out the common factor k and simplifying, you'll get a quadratic equation in terms of r. Solving this equation will give the value of r where the fields cancel out.
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- Let r be the distance from q1 where the electric field is zero.
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- Set up the equation q1/r² = q2/(d-r)².
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- Solve for r by cross multiplying and rearranging the equation into a standard quadratic form.
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- Find the roots of the quadratic equation. One root will be physically meaningful as it will be less than d and that root will be your answer.
By applying these steps, you should be able to calculate the precise distance from the first charge at which the electric field intensity is zero.