Question

A block of mass m with a charge q is placed on a smooth horizontal table and is connected to a wall through an unstressed spring of spring constant k, as shown in the figure. A horizontal electric field E, parallel to the spring, is switched on. Find the amplitude of the resulting SHM of the block.
Figure

Answer 1

Explanation:

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Answer 2

The amplitude of the resulting SHM of the block is,  $-\frac{q E}{k}$.

Explanation:        

Step 1:

          Let block’s mass = m      

          Let block’s charge  = q

          Connected spring constant to block and wall = k

          Horizontal electric field = E

Step 2:

• When applied with horizontal electric field, the accelerating force acts on the block in the right direction.
• Spring force balances this force, since spring is also related to block.
• Let, x is spring peak extension.

So, spring force =  electrostatic force

                      -kx = qE

                        $x= - \frac{q E}{k}$

We know that, the ultimate spring extension is just amplitude.

Thus, the amplitude is $-\frac{q E}{k}$.