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Assertion Maganetic field (B) and elec...

Assertion Maganetic field (B) and electric field (E) are present in a this region. Net force on a charged particle in this region is zero , if
`E=Bxx v`
Reason E/B has the dimensions of velocity.

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The correct Answer is:
To solve the given question, we need to analyze both the assertion and the reason provided. ### Step 1: Understanding the Assertion The assertion states that in a region where both a magnetic field (B) and an electric field (E) are present, the net force on a charged particle is zero if the relationship \( E = B \times v \) holds true. **Explanation**: The force on a charged particle in an electric field is given by: \[ F_E = qE \] where \( q \) is the charge of the particle. The force on a charged particle in a magnetic field is given by: \[ F_B = q(v \times B) \] where \( v \) is the velocity of the particle. For the net force to be zero: \[ F_E + F_B = 0 \] This implies: \[ qE + q(v \times B) = 0 \] Dividing through by \( q \) (assuming \( q \neq 0 \)): \[ E + (v \times B) = 0 \] This can be rearranged to: \[ E = - (v \times B) \] If we assume that \( E = B \times v \), it indicates that the electric force and the magnetic force are equal in magnitude but opposite in direction, leading to a net force of zero. ### Step 2: Understanding the Reason The reason states that the ratio \( \frac{E}{B} \) has the dimensions of velocity. **Explanation**: The dimensions of electric field \( E \) are: \[ [E] = \frac{ML^2}{T^3I} \] The dimensions of magnetic field \( B \) are: \[ [B] = \frac{ML}{T^2I} \] Now, calculating the dimensions of \( \frac{E}{B} \): \[ \frac{E}{B} = \frac{\frac{ML^2}{T^3I}}{\frac{ML}{T^2I}} = \frac{L^2}{T^3} \cdot \frac{T^2I}{L} = \frac{L}{T} \] This is indeed the dimension of velocity. ### Conclusion Both the assertion and the reason are correct. However, the reason does not directly explain the assertion; it merely provides a dimensional analysis. ### Final Answer - **Assertion**: True - **Reason**: True - **Explanation**: The reason is not a correct explanation of the assertion.
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