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The electric field in a region of space ...

The electric field in a region of space is given by `E=5hati+2hatjN//C`. The flux of E due ot this field through an area `1m^2`lying in the y-z plane, in SI units is

A

5

B

10

C

2

D

`5sqrt(29)`

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The correct Answer is:
To solve the problem, we will calculate the electric flux through an area of 1 m² lying in the y-z plane given the electric field \( \mathbf{E} = 5 \hat{i} + 2 \hat{j} \, \text{N/C} \). ### Step-by-Step Solution: 1. **Identify the Area Vector**: The area lies in the y-z plane. The normal vector (area vector) to this plane is directed along the x-axis. Therefore, the area vector can be represented as: \[ \mathbf{A} = 1 \hat{i} \, \text{m}^2 \] 2. **Write the Electric Field Vector**: The electric field is given as: \[ \mathbf{E} = 5 \hat{i} + 2 \hat{j} \, \text{N/C} \] 3. **Calculate the Electric Flux**: The electric flux \( \Phi_E \) through the surface is given by the dot product of the electric field vector and the area vector: \[ \Phi_E = \mathbf{E} \cdot \mathbf{A} \] 4. **Perform the Dot Product**: Substitute the vectors into the dot product: \[ \Phi_E = (5 \hat{i} + 2 \hat{j}) \cdot (1 \hat{i}) \] Using the properties of dot products: \[ \Phi_E = (5 \hat{i} \cdot \hat{i}) + (2 \hat{j} \cdot \hat{i}) = 5 \cdot 1 + 2 \cdot 0 = 5 + 0 = 5 \] 5. **Final Result**: The electric flux through the area is: \[ \Phi_E = 5 \, \text{N m}^2/\text{C} \] ### Conclusion: The electric flux through the area of 1 m² lying in the y-z plane is \( 5 \, \text{N m}^2/\text{C} \). ---

To solve the problem, we will calculate the electric flux through an area of 1 m² lying in the y-z plane given the electric field \( \mathbf{E} = 5 \hat{i} + 2 \hat{j} \, \text{N/C} \). ### Step-by-Step Solution: 1. **Identify the Area Vector**: The area lies in the y-z plane. The normal vector (area vector) to this plane is directed along the x-axis. Therefore, the area vector can be represented as: \[ \mathbf{A} = 1 \hat{i} \, \text{m}^2 ...
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DC PANDEY ENGLISH-ELECTROSTATICS-Level 1 Objective
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  2. Charges Q, 2Q, and -Q are given to three concentric conducting spherei...

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  11. A conducting shell S1 having a charge Q is surrounded by an uncharged ...

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