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For two charges 3C and -3C separated by 1cm and are located at distances 5cm and 7cm respectively from the point P, then the distance between their midpoint and the point P will be
- a)5.91
- b)12.6
- c)2
- d)9
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
For two charges 3C and -3C separated by 1cm and are located at distanc...
Answer: a
Explanation: For a distant point P, the R1 and R2 will approximately be equal.
R1 = R2 = r, where r is the distance between P and the midpoint of the two charges. Thus they are in geometric progression, R1R2=r2
Now, r2 = 5 x 7 = 35. We get r = 5.91cm.
Explanation: For a distant point P, the R1 and R2 will approximately be equal.
R1 = R2 = r, where r is the distance between P and the midpoint of the two charges. Thus they are in geometric progression, R1R2=r2
Now, r2 = 5 x 7 = 35. We get r = 5.91cm.
Most Upvoted Answer
For two charges 3C and -3C separated by 1cm and are located at distanc...
Given information:
- Two charges of magnitude 3C and -3C are separated by a distance of 1cm.
- The point P is located at distances of 5cm and 7cm from the charges, respectively.
To find:
The distance between the midpoint of the charges and the point P.
Calculating the midpoint:
The midpoint of two charges is the point equidistant from both charges. Let's calculate the midpoint using the formula:
Midpoint = (x₁ + x₂) / 2, (y₁ + y₂) / 2
Here, the charges are located on the x-axis, so y₁ and y₂ will be 0.
The coordinates of the charges are:
Charge 1: (x₁, y₁) = (5cm, 0)
Charge 2: (x₂, y₂) = (7cm, 0)
Using the midpoint formula:
Midpoint = (5cm + 7cm) / 2, (0 + 0) / 2
Midpoint = (12cm) / 2, 0
Midpoint = 6cm, 0
Calculating the distance between the midpoint and point P:
The distance between two points can be calculated using the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Here, the coordinates of the midpoint are (6cm, 0), and the coordinates of point P are (x, 0) (since the point P is located on the x-axis).
Using the distance formula:
Distance = √((x - 6cm)² + 0²)
Substituting the given distances for x:
Distance = √((5cm - 6cm)² + 0²) for point P₁
Distance = √((-1cm)²) = √(1cm²) = 1cm
Distance = √((7cm - 6cm)² + 0²) for point P₂
Distance = √((1cm)²) = √(1cm²) = 1cm
The distance between the midpoint and point P is the average of these two distances:
Distance = (1cm + 1cm) / 2 = 2cm / 2 = 1cm
Therefore, the distance between the midpoint of the charges and point P is 1cm, which corresponds to option C.
- Two charges of magnitude 3C and -3C are separated by a distance of 1cm.
- The point P is located at distances of 5cm and 7cm from the charges, respectively.
To find:
The distance between the midpoint of the charges and the point P.
Calculating the midpoint:
The midpoint of two charges is the point equidistant from both charges. Let's calculate the midpoint using the formula:
Midpoint = (x₁ + x₂) / 2, (y₁ + y₂) / 2
Here, the charges are located on the x-axis, so y₁ and y₂ will be 0.
The coordinates of the charges are:
Charge 1: (x₁, y₁) = (5cm, 0)
Charge 2: (x₂, y₂) = (7cm, 0)
Using the midpoint formula:
Midpoint = (5cm + 7cm) / 2, (0 + 0) / 2
Midpoint = (12cm) / 2, 0
Midpoint = 6cm, 0
Calculating the distance between the midpoint and point P:
The distance between two points can be calculated using the distance formula:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Here, the coordinates of the midpoint are (6cm, 0), and the coordinates of point P are (x, 0) (since the point P is located on the x-axis).
Using the distance formula:
Distance = √((x - 6cm)² + 0²)
Substituting the given distances for x:
Distance = √((5cm - 6cm)² + 0²) for point P₁
Distance = √((-1cm)²) = √(1cm²) = 1cm
Distance = √((7cm - 6cm)² + 0²) for point P₂
Distance = √((1cm)²) = √(1cm²) = 1cm
The distance between the midpoint and point P is the average of these two distances:
Distance = (1cm + 1cm) / 2 = 2cm / 2 = 1cm
Therefore, the distance between the midpoint of the charges and point P is 1cm, which corresponds to option C.
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For two charges 3C and -3C separated by 1cm and are located at distances 5cm and 7cm respectively from the point P, then the distance between their midpoint and the point P will bea)5.91b)12.6c)2d)9Correct answer is option 'A'. Can you explain this answer?
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