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A point charge is located at the origin in free space. The work done in carrying a charge 10 C from point A (r = 4 cm, θ = π/6 , Ø  = π/4) to B (r = 4 cm, θ = π/3 , Ø  = π/6) is 
  • a)
    0.45 μJ
  • b)
    0.32 μJ
  • c)
    -0.45 μJ
  • d)
    0
Correct answer is option 'D'. Can you explain this answer?
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Given information:
- A point charge is located at the origin in free space.
- Charge at point A: 10 C
- Position of point A: r = 4 cm, θ = π/6, φ = π/4
- Position of point B: r = 4 cm, θ = π/3, φ = π/6

To calculate the work done in carrying the charge from point A to point B, we can use the formula:

W = q * ΔV

where:
- W is the work done
- q is the charge
- ΔV is the change in potential energy

Step 1: Calculate the potential energy change

The potential energy change can be calculated using the formula:

ΔV = V_B - V_A

where:
- V_B is the potential at point B
- V_A is the potential at point A

Step 2: Calculate the potentials at points A and B

The potential at a point due to a point charge can be calculated using the formula:

V = k * (q / r)

where:
- V is the potential
- k is the Coulomb's constant (9 x 10^9 Nm^2/C^2)
- q is the charge
- r is the distance from the point charge

Using this formula, we can calculate the potentials at points A and B.

Step 3: Calculate the potential energy change

Now that we have the potentials at points A and B, we can calculate the potential energy change ΔV = V_B - V_A.

Step 4: Calculate the work done

Finally, we can calculate the work done using the formula W = q * ΔV.

Calculations:

Step 2: Calculate the potentials at points A and B

Using the formula V = k * (q / r), we can calculate the potentials at points A and B.

V_A = (9 x 10^9 Nm^2/C^2) * (10 C / 0.04 m) = 2.25 x 10^12 Nm/C
V_B = (9 x 10^9 Nm^2/C^2) * (10 C / 0.04 m) = 2.25 x 10^12 Nm/C

Step 3: Calculate the potential energy change

ΔV = V_B - V_A = (2.25 x 10^12 Nm/C) - (2.25 x 10^12 Nm/C) = 0

Step 4: Calculate the work done

W = q * ΔV = (10 C) * (0) = 0

Therefore, the work done in carrying the charge from point A to point B is 0 J.
Hence, the correct answer is option 'D' (0 J).
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A point charge is located at the origin in free space. The work done in carrying a charge 10 C from point A(r = 4 cm, θ = π/6, Ø =π/4) to B(r = 4 cm, θ = π/3, Ø =π/6) isa)0.45μJb)0.32 μJc)-0.45 μJd)0Correct answer is option 'D'. Can you explain this answer?
Question Description
A point charge is located at the origin in free space. The work done in carrying a charge 10 C from point A(r = 4 cm, θ = π/6, Ø =π/4) to B(r = 4 cm, θ = π/3, Ø =π/6) isa)0.45μJb)0.32 μJc)-0.45 μJd)0Correct answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A point charge is located at the origin in free space. The work done in carrying a charge 10 C from point A(r = 4 cm, θ = π/6, Ø =π/4) to B(r = 4 cm, θ = π/3, Ø =π/6) isa)0.45μJb)0.32 μJc)-0.45 μJd)0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A point charge is located at the origin in free space. The work done in carrying a charge 10 C from point A(r = 4 cm, θ = π/6, Ø =π/4) to B(r = 4 cm, θ = π/3, Ø =π/6) isa)0.45μJb)0.32 μJc)-0.45 μJd)0Correct answer is option 'D'. Can you explain this answer?.
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