CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Work Done When Force Is Varying

Two identical...

Question

Two identical spheres having charges $+ q_{1}$ and $+ q_{2}$ are kept at a distance "d". These two are brought in contact with an insulated handle and again separated to the same distance. Find the force $F_{2}$ between them in terms of initial force $F_{1}$ .

A

F_{2} = F_{1} \frac{(q_{1} + q_{2})^{3}}{4 q_{1}^{2} q_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

F_{2} = F_{1} \frac{(q_{1} + q_{2})^{3}}{4 q_{1} q_{2}^{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

F_{2} = F_{1} \frac{(q_{1} + q_{2})}{4 q_{1}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

F_{2} = F_{1} \frac{(q_{1} + q_{2})^{2}}{4 q_{1} q_{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $F_{2} = F_{1} \frac{(q_{1} + q_{2})^{2}}{4 q_{1} q_{2}}$
Let initially, charges are separated by a distance $^{'} d^{'} .$
Then, according to Coulomb's Law,
$F_{1} = \frac{k q_{1} q_{2}}{d^{2}}$
$\Rightarrow d^{2} = \frac{k q_{1} q_{2}}{F_{1}}$ ...(i)

Now, when both the identical spheres are brought in contact, then charge on each sphere is average of initial charge on each sphere.
i.e, $Q = \frac{q_{1} + q_{2}}{2}$ on each sphere.

Now, Force between them i.e, $F_{2}$ is
$F_{2} = \frac{k Q^{2}}{d^{2}}$
From (i), $d^{2} = \frac{k q_{1} q_{2}}{F_{1}}$
So, $F_{2} = \frac{k (q_{1} + q_{2})^{2}}{k q_{1} q_{2} \times 4} \times F_{1}$
$F_{2} = F_{1} \times \frac{(q_{1} + q_{2})^{2}}{4 q_{1} q_{2}}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Two identical spheres having charges

+ q_{1}

+ q_{2}

are kept at a distance "d". These two are brought in contact with an insulated handle and again separated to the same distance. Find the force

F_{2}

between them in terms of initial force

F_{1}

Q. Two identical small conducting spheres carry charges of

Q_{1}

Q_{2}

Q_{1} >> Q_{2}

. The spheres are d distance apart. The force they exert on each other is

F_{1}

. The spheres are made to touch each other and then separated by a distance d. The force they exert on each other now is

F_{2}

F_{1} / F_{2}

Q_{1}

O

inside a hollow conducting sphere having inner and outer radii as

10 m

11 m

as shown in the figure. The force experienced by

Q_{2}

P

F_{1}

Q_{1}

is placed at the center and force experienced by

Q_{2}

Q_{1}

O

F_{2}

\frac{F_{1}}{F_{2}}

Q. Two small conducting sphere of equal have charges

10 μ C

- 20 μ C

are placed at a distance

^{'} R^{'}

from each other experience force

F_{1}

. If the are brought in contact and separated to the same distance, they experience force

F_{2}

F_{1}

F_{2}

Q. Two small conducting spheres of equal radius have charges

+ 10 μ C

- 20 μ C

respectively and placed at a distance R from each other experience force

F_{1}

. If they are brought in contact and separated to the same distance, they experience force

F_{2}

F_{1}

F_{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

So You Think You Know Work?

PHYSICS

Watch in App

explore_more_icon

Explore more

Work Done When Force Is Varying

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon