Question

two identical spheres A and B have equal charge . they repel each other with a force 103N, when they are placed 10cm apart in a medium of dielectric constant 7. determinr the chargr on each sphere

Answer 1

Explanation:

They repel each other with a force 103N, when they are placed 10cm apart in a medium of dielectric constant 7 . Determine the charge on each sphere.

Answer 2

Given:

Two identical spheres A and B have equal charge . they repel each other with a force 10³N, when they are placed 10cm apart in a medium of dielectric constant 7.

To find:

Charge on each sphere.

Calculation:

We know that expression of electrostatic force

$force = \dfrac{1}{4\pi \epsilon_{0} } \bigg \{ \dfrac{(q1)(q2)}{ {r}^{2} } \bigg \}$

Here , q1 = q2 = q ......(let)

$= > force = \dfrac{1}{4\pi \epsilon_{0}k } \bigg \{ \dfrac{q \times q}{ {r}^{2} } \bigg \}$

$= > force = \dfrac{1}{4\pi \epsilon_{0}k } \bigg \{ \dfrac{ {q}^{2} }{ {r}^{2} } \bigg \}$

$= > {10}^{3} = \dfrac{1}{4\pi \epsilon_{0}k } \bigg \{ \dfrac{ {q}^{2} }{ {( \frac{10}{100}) }^{2}} \bigg \}$

$= > {10}^{3} = \dfrac{1}{4\pi \epsilon_{0}k } \bigg \{ \dfrac{ {q}^{2} }{ {10}^{ - 2} } \bigg \}$

$= > {10}^{3} = \dfrac{9 \times {10}^{9}}{7} \times \bigg \{ \dfrac{ {q}^{2} }{ {10}^{ - 2} } \bigg \}$

$= > {10}^{3} = \dfrac{9 \times {10}^{11}}{7} \times \bigg \{ {q}^{2} \bigg \}$

$= > {10}^{ - 8} = \dfrac{9 }{7} \times \bigg \{ {q}^{2} \bigg \}$

$= > {q}^{2} = \dfrac{7 \times {10}^{ - 8} }{9}$

$= > q = \dfrac{ \sqrt{7} \times {10}^{ - 4} }{3}$

$= > q = 0.88 \times {10}^{ - 4} \: coulombs$

So, final answer is:

$\boxed{ \red{q = 0.88 \times {10}^{ - 4} \: coulombs}}$