The work done in bringing a unit positive charge from infinite distanc...
Electric potential at a point in an electric field is defined as the work done in bringing a unit positive charge from infinity to that point.
Or, V = W/q
Since charge is of magnitude unity, Hence electric potential at that point will be equal to the workdone ∴ ϕ = W
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The work done in bringing a unit positive charge from infinite distanc...
**Explanation:**
To understand why the correct answer is option B, let's break down the concepts step by step.
**1. Work Done (W):**
The work done in bringing a unit positive charge from infinite distance to a point at distance x from a positive charge Q is given as W. This means that a force must have been applied to move the charge against the electric field created by the positive charge Q.
**2. Electric Potential (V):**
The electric potential at a point in an electric field is defined as the amount of work done in bringing a unit positive charge from infinity to that point. It is also known as the electric potential energy per unit charge.
**3. Relationship between Work Done and Electric Potential:**
The work done (W) in bringing a unit positive charge from infinity to a point at distance x from a positive charge Q is equal to the change in electric potential energy (ΔPE) of the charge. Mathematically, this can be expressed as:
W = ΔPE
**4. Electric Potential at a Point (V):**
The electric potential at a point, denoted by V, is defined as the electric potential energy per unit charge. Mathematically, it can be expressed as:
V = PE / q
where V is the electric potential, PE is the electric potential energy, and q is the charge.
**5. Electric Potential due to a Point Charge:**
The electric potential (V) due to a point charge Q at a distance x can be calculated using the formula:
V = kQ / x
where V is the electric potential, Q is the charge, x is the distance, and k is the Coulomb's constant.
**6. Equating Work Done and Change in Electric Potential Energy:**
Since the work done (W) in bringing a unit positive charge from infinity to a point at distance x from a positive charge Q is equal to the change in electric potential energy (ΔPE) of the charge, we can equate them:
W = ΔPE
**7. Equating Change in Electric Potential Energy and Electric Potential:**
Since the change in electric potential energy (ΔPE) is equal to the product of the charge (q) and the change in electric potential (ΔV), we can express it as:
ΔPE = qΔV
**8. Substituting Equations:**
Substituting the equations from step 6 and step 7, we get:
W = qΔV
**9. Simplifying the Equation:**
Since we are considering a unit positive charge, the charge (q) is equal to 1. Therefore, the equation becomes:
W = ΔV
**10. Conclusion:**
From the equation derived in step 9, we can conclude that the work done (W) in bringing a unit positive charge from infinity to a point at distance x from a positive charge Q is equal to the change in electric potential (ΔV) at that point. Therefore, the potential at that point is equal to the work done, which is option B.