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Assertion: At a point electric potential...

Assertion: At a point electric potential is decreasing along x-axis at a rate of `10 V//m`. Therefore, x-component of electric field at this point should be `10 V//m` along x-axis.
Reason: Magnitude of `E_x=(delV)/(delx)`

A

If both Assertion and Reason are true but Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the assertion and the reason provided in the question. ### Step-by-Step Solution: 1. **Understanding Electric Potential and Electric Field**: - Electric potential (V) is a scalar quantity that represents the potential energy per unit charge at a point in an electric field. - The electric field (E) is a vector quantity that represents the force per unit charge experienced by a positive test charge placed in the field. 2. **Relationship Between Electric Field and Electric Potential**: - The relationship between the electric field and electric potential is given by the equation: \[ E_x = -\frac{dV}{dx} \] - Here, \(E_x\) is the x-component of the electric field, and \(\frac{dV}{dx}\) is the rate of change of electric potential with respect to x. 3. **Given Information**: - The problem states that the electric potential is decreasing along the x-axis at a rate of \(10 \, \text{V/m}\). This means: \[ \frac{dV}{dx} = -10 \, \text{V/m} \] - Since the potential is decreasing, the negative sign indicates that as we move in the positive x-direction, the potential decreases. 4. **Calculating the x-component of Electric Field**: - Using the relationship \(E_x = -\frac{dV}{dx}\): \[ E_x = -(-10 \, \text{V/m}) = 10 \, \text{V/m} \] - Therefore, the x-component of the electric field at that point is \(10 \, \text{V/m}\) along the x-axis. 5. **Conclusion**: - The assertion states that the x-component of the electric field should be \(10 \, \text{V/m}\) along the x-axis, which we have confirmed to be true. - The reason provided is also true as it correctly describes the relationship between electric field and electric potential. ### Final Answer: - **Assertion**: True - **Reason**: True, but it does not correctly explain the assertion.

To solve the problem, we need to analyze the assertion and the reason provided in the question. ### Step-by-Step Solution: 1. **Understanding Electric Potential and Electric Field**: - Electric potential (V) is a scalar quantity that represents the potential energy per unit charge at a point in an electric field. - The electric field (E) is a vector quantity that represents the force per unit charge experienced by a positive test charge placed in the field. ...
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