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The answer to each of the following ques...

The answer to each of the following questions is a single-digit integer ranging from 0 to 9. Darken the correct digit.
A metal plate with total charge Q on it, is placed parallel to a dielectric slab of same area. Let q be the charge appearing on the surface of dielectric whose dielectric constant is 2. Calculate `Q//q`.

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To solve the problem, we need to find the ratio \( \frac{Q}{q} \), where \( Q \) is the total charge on the metal plate and \( q \) is the charge appearing on the surface of the dielectric slab. ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have a metal plate with a total charge \( Q \). - This plate is placed parallel to a dielectric slab with a dielectric constant \( k = 2 \). 2. **Charge Induction on the Dielectric**: - When a metal plate with charge \( Q \) is placed near a dielectric, it induces a charge \( q \) on the surface of the dielectric. - The induced charge \( q \) can be calculated using the formula: \[ q = Q \left(1 - \frac{1}{k}\right) \] - Here, \( k \) is the dielectric constant of the material. 3. **Substituting the Dielectric Constant**: - We know that \( k = 2 \). - Substitute \( k \) into the equation: \[ q = Q \left(1 - \frac{1}{2}\right) \] - Simplifying this gives: \[ q = Q \left(\frac{1}{2}\right) \] 4. **Finding the Ratio \( \frac{Q}{q} \)**: - Now, we need to find the ratio \( \frac{Q}{q} \): \[ \frac{Q}{q} = \frac{Q}{Q \left(\frac{1}{2}\right)} = \frac{1}{\frac{1}{2}} = 2 \] 5. **Final Answer**: - Therefore, the value of \( \frac{Q}{q} \) is \( 2 \). ### Final Result: \[ \frac{Q}{q} = 2 \]

To solve the problem, we need to find the ratio \( \frac{Q}{q} \), where \( Q \) is the total charge on the metal plate and \( q \) is the charge appearing on the surface of the dielectric slab. ### Step-by-Step Solution: 1. **Understanding the Setup**: - We have a metal plate with a total charge \( Q \). - This plate is placed parallel to a dielectric slab with a dielectric constant \( k = 2 \). ...
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