Question

a charge Q is placed at the centre of a square if electric field intensity due to the charge at the corners of the square is E1 and the intensity at the midpoint of the side of square is E2,then the ratio of E1/E2 will be
$(1)1 \div2 \sqrt{2}$
$(2) \sqrt{2}$
$(3)1 \div 2$
$(4)2$

Answer 1

The ratio of the electric field $\bold{\frac{E 1}{E 2}\ \mathrm{is}\ \frac{1}{2}}$.

Solution:

The midpoint mentioned in the question which means midpoint is the side of the square.

Distance of the corner of square and the mid of square is $\frac{a}{\sqrt{2}}$, where it is a side of square.

Distance between midpoint of the side and centre of square is $\frac{a}{2}$

$\mathrm{E} 1=\frac{2 q}{\left[(4 \pi \varepsilon 0) a^{2}\right]}$

$\mathrm{E} 2=\frac{4 q}{\left[(4 \pi \varepsilon 0) a^{2}\right]}$

Now, the ratio of the charges is given by   $\frac{E 1}{E_{2}}=\frac{1}{2}$.

Answer 2

Answer:1/2

Explanation:The ratio of the electric field .

Solution:

The midpoint mentioned in the question which means midpoint is the side of the square.

Distance of the corner of square and the mid of square is , where it is a side of square.

Distance between midpoint of the side and centre of square is

Now, the ratio of the charges is given by 1/2  .