A charge +Q and a charge -2Q are a distance 3x apart. Point P is on the line joining thecharges, at a distance x from +Q.P+Q −2Qx 2xThe magnitude of the electric field produced at P by the charge +Q alone is E.What is the total electric field at P
Question
A charge +Q and a charge -2Q are a distance 3x apart. Point P is on the line joining thecharges, at a distance x from +Q.P+Q −2Qx 2xThe magnitude of the electric field produced at P by the charge +Q alone is E.What is the total electric field at P
Solution
The electric field at a point due to a charge is given by the formula:
E = kQ/r^2
where:
- E is the electric field,
- k is Coulomb's constant (approximately 8.99 x 10^9 N m^2/C^2),
- Q is the charge,
- r is the distance from the charge to the point.
Given that the electric field at point P due to charge +Q alone is E, we can use this information to find the electric field at point P due to charge -2Q.
First, we calculate the distance from -2Q to point P. This distance is 2x (since P is x away from +Q and +Q and -2Q are 3x apart).
Next, we use the formula to find the electric field at P due to -2Q:
E' = k(-2Q)/(2x)^2 E' = -2kQ/(4x^2) E' = -kQ/(2x^2)
Since the electric field due to +Q is E = kQ/x^2, we can substitute this into the equation for E':
E' = -E/2
The total electric field at P is the sum of the electric fields due to +Q and -2Q. Since these fields are in opposite directions (because the charges are opposite), we subtract E' from E:
E_total = E - E' E_total = E - (-E/2) E_total = E + E/2 E_total = 1.5E
So, the total electric field at point P is 1.5E.
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