
Assuming mass m of the charged particle, find the time period of oscillation.

Answer
501.9k+ views
1 likes
Hint: The acceleration of a charge is equal to the product of square of angular frequency and the displacement. The force exerted on the charge is equal to the product of charge and the net electric field. By equating it with Newton’s second law, we can get acceleration and from acceleration we can get angular frequency and finally the time period.
Formula used:
Newton’s second law of motion:
Force on a charge in electric field:
Acceleration of an oscillating charge is given as
Time period is related to angular frequency by following relation:
Here all the symbols have their usual meaning.
Complete answer:
In the given diagram, we have two charges of the same magnitude at (-a,0,0) and (a,0,0). At a point along the line passing through the centre of the line joining the two charges, the various components of the electric field are shown. Since the charges have the same magnitude their electric fields also have the same values.
Now the horizontal components of the electric field cancel each other while the vertical components get added up. Hence, the net electric field is given as
The force due to this electric field on a charged particle of mass m is given as
If x << a then,
Now using Newton’s second law, we get
We denote acceleration by A.
As we know that acceleration of a charged particle undergoing oscillations is given as follows:
The time period is given as
Hence, the correct answer is option B.
Note:
In this question the charge that is undergoing oscillation is a positive test charge. But in case, we had a negative charge then the directions of resultant forces would have been opposite to that for the positive charge. But the final answer would still remain the same in magnitude.
Formula used:
Newton’s second law of motion:
Force on a charge in electric field:
Acceleration of an oscillating charge is given as
Time period is related to angular frequency by following relation:
Here all the symbols have their usual meaning.
Complete answer:
In the given diagram, we have two charges of the same magnitude at (-a,0,0) and (a,0,0). At a point along the line passing through the centre of the line joining the two charges, the various components of the electric field are shown. Since the charges have the same magnitude their electric fields also have the same values.
Now the horizontal components of the electric field cancel each other while the vertical components get added up. Hence, the net electric field is given as
The force due to this electric field on a charged particle
If x << a then,
Now using Newton’s second law, we get
We denote acceleration by A.
As we know that acceleration of a charged particle undergoing oscillations is given as follows:
The time period is given as
Hence, the correct answer is option B.
Note:
In this question the charge that is undergoing oscillation is a positive test charge. But in case, we had a negative charge then the directions of resultant forces would have been opposite to that for the positive charge. But the final answer would still remain the same in magnitude.
Recently Updated Pages
Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Social Science: Engaging Questions & Answers for Success

Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Trending doubts
How many moles and how many grams of NaCl are present class 11 chemistry CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

Plants which grow in shade are called A Sciophytes class 11 biology CBSE

A renewable exhaustible natural resource is A Petroleum class 11 biology CBSE

In which of the following gametophytes is not independent class 11 biology CBSE

Find the molecular mass of Sulphuric Acid class 11 chemistry CBSE
