Given two point charges, Q and 2Q, a distance l apart, is there a point along the straight line that passes through them where E = 0 when their signs are (a) opposite, (b) the same? If yes, state roughly where this point will be.
Part(a)To Determine:
A point along the straight line that passes through two charges where when the signs of the charges are opposite.
Answer to Problem 22Q
Solution:
The point along the straight line joining the two charges where lies outside of the charges and at a distance of away from the weaker charge and away from the stronger charge if the charges have opposite signs and placed distance apart.
Explanation of Solution
Given Info:
The two charges and are placed distance apart.
Formula Used:
The electric field at a point distance apart from a point charge is given by,
Calculation:
Let be negative and be positive. Since the two charges are of opposite signs then the point at which lies outside of the charges.
The electric fields at the point P due to the two charges are in opposite direction.
The point P is at a distance of from the charge .
If at P, then at the point P
That is,
Therefore, and
Solving we get,
The point P lies at away from and away from
If two charges having opposite sign are placed at a distance apart, then the point along the straight line joining the two charges where lies outside of the charges and at a distance of away from the weaker charge and away from the stronger charge.
Part(b)To Determine:
A point along the straight line that passes through two charges where when the signs of the charges are the same.
Answer to Problem 22Q
Solution:
The point along the straight line joining the two charges where lies in between the charges and at a distance of away from the weaker charge and away from the stronger charge if the charges have same sign and placed distance apart.
Explanation of Solution
Given Info:
The two charges and are placed distance apart.
Formula Used:
The electric field at a point distance apart from a point charge is given by,
Calculation:
Let both and are positive. Since the two charges are of same sign then
the point at which lies in between the charges.
The electric fields at the point P due to the two charges are in opposite direction.
The point P is at a distance of from the charge .
If
at P, then at the point P
That is,
Therefore, and
Solving we get,
The point P lies at away from and away from
If two charges having same sign are placed at a distance apart, then the point along the straight line joining the two charges where lies in between the charges and at a distance of away from the weaker charge and away from the stronger charge.
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Physics: Principles with Applications
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