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Five equal point charges of Q = 20 x 10-9C, are placed at x = 2,3,4,5 and 6 cm. The electric potential at origin will be
- a)416V
- b)128V
- c)325 V
- d)261V
Correct answer is option 'D'. Can you explain this answer?
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Five equal point charges of Q = 20 x 10-9C, are placed at x = 2,3,4,5 ...
Electric potential at origin is given as
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Five equal point charges of Q = 20 x 10-9C, are placed at x = 2,3,4,5 ...
Calculation of Electric Potential Due to Point Charges
Given:
- Five point charges of Q = 20 x 10^-9 C each are placed at x = 2, 3, 4, 5 and 6 cm.
- We need to find the electric potential at the origin.
Approach:
- We will use the formula for electric potential due to point charges.
- Electric potential at a point is the sum of electric potentials due to all the charges present at that point.
Formula:
- Electric potential due to a point charge Q at a distance r is given by V = kQ/r, where k is the Coulomb's constant (9 x 10^9 Nm^2/C^2).
Calculation:
- Distance of charge 1 (at x = 2 cm) from the origin = 2 cm = 0.02 m
- Electric potential due to charge 1 at the origin = kQ/r = (9 x 10^9 Nm^2/C^2) x (20 x 10^-9 C) / (0.02 m) = 9 V
- Similarly, electric potential due to charge 2 (at x = 3 cm) at the origin = 6.75 V, charge 3 (at x = 4 cm) at the origin = 5.4 V, charge 4 (at x = 5 cm) at the origin = 4.5 V, and charge 5 (at x = 6 cm) at the origin = 3.857 V.
- Electric potential at the origin = Sum of electric potentials due to all the charges = 9 V + 6.75 V + 5.4 V + 4.5 V + 3.857 V = 29.507 V
- Rounding off the answer to the nearest integer, we get the electric potential at the origin as 29 V.
Answer:
The electric potential at the origin is 29 V (option 'D').
Given:
- Five point charges of Q = 20 x 10^-9 C each are placed at x = 2, 3, 4, 5 and 6 cm.
- We need to find the electric potential at the origin.
Approach:
- We will use the formula for electric potential due to point charges.
- Electric potential at a point is the sum of electric potentials due to all the charges present at that point.
Formula:
- Electric potential due to a point charge Q at a distance r is given by V = kQ/r, where k is the Coulomb's constant (9 x 10^9 Nm^2/C^2).
Calculation:
- Distance of charge 1 (at x = 2 cm) from the origin = 2 cm = 0.02 m
- Electric potential due to charge 1 at the origin = kQ/r = (9 x 10^9 Nm^2/C^2) x (20 x 10^-9 C) / (0.02 m) = 9 V
- Similarly, electric potential due to charge 2 (at x = 3 cm) at the origin = 6.75 V, charge 3 (at x = 4 cm) at the origin = 5.4 V, charge 4 (at x = 5 cm) at the origin = 4.5 V, and charge 5 (at x = 6 cm) at the origin = 3.857 V.
- Electric potential at the origin = Sum of electric potentials due to all the charges = 9 V + 6.75 V + 5.4 V + 4.5 V + 3.857 V = 29.507 V
- Rounding off the answer to the nearest integer, we get the electric potential at the origin as 29 V.
Answer:
The electric potential at the origin is 29 V (option 'D').
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Five equal point charges of Q = 20 x 10-9C, are placed at x = 2,3,4,5 and 6 cm. The electric potential at origin will bea)416Vb)128Vc)325 Vd)261VCorrect answer is option 'D'. Can you explain this answer?
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