a. Can a vector have nonzero magnitude if a component is zero? If no, why not? If yes, give an example. b. Can a vector have zero magnitude and a nonzero component? If no, why not? If yes, give an example.
a. Can a vector have nonzero magnitude if a component is zero? If no, why not? If yes, give an example. b. Can a vector have zero magnitude and a nonzero component? If no, why not? If yes, give an example.
a. Can a vector have nonzero magnitude if a component is zero? If no, why not? If yes, give an example.
b. Can a vector have zero magnitude and a nonzero component? If no, why not? If yes, give an example.
a.
Expert Solution
To determine
A vector have a nonzero magnitude if a component is zero.
Answer to Problem 1CQ
Vector can have nonzero magnitude if a component is zero is explained with an example.
Explanation of Solution
Let, Vector be
v→ and components of
v→ be
v1,v2,v3,.....vn.
Write the expression to find the magnitude of vector.
|v→|=v12+v22+v32+...+vn2
So, Magnitude of vector
|v→| is zero if and only iff all the components are zero. If any one of the component result with non zero, then vector will have nonzero magnitude.
Example:
Consider the two dimensional vector as follows.
v→=5i + 0j
In this vector the y component is 0 but still the magnitude is 5. A vector only has zero magnitude when all its components are 0.
Thus, vector can have nonzero magnitude if a component is zero.
Conclusion:
Hence, vector can have nonzero magnitude if a component is zero is explained with an example.
b.
Expert Solution
To determine
A vector have a zero magnitude and a nonzero component.
Answer to Problem 1CQ
Vector cannot have zero magnitude with non zero component is explained.
Explanation of Solution
As explained in part (a), the magnitude of vector is zero if and only iff all the components is zero. If any of the component is nonzero then magnitude of the vector result with nonzero.
Therefore vector cannot have zero magnitude with non zero component.
Example:
Consider a vector as follows.
v→=v1i+v2j+v3k
Find the magnitude of vector
v→.
|v→|=v12+v22+v32
From the above expression, if
v1+v2+v3 is non zero value, then magnitude of
v→ will also be non zero.
Conclusion:
Hence, cannot have zero magnitude with non zero component is explained.
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Four capacitors are connected as shown in the figure below. (Let C = 12.0 µF.)
A circuit consists of four capacitors. It begins at point a before the wire splits in two directions. On the upper split, there is a capacitor C followed by a 3.00 µF capacitor. On the lower split, there is a 6.00 µF capacitor. The two splits reconnect and are followed by a 20.0 µF capacitor, which is then followed by point b.
(a) Find the equivalent capacitance between points a and b. µF(b) Calculate the charge on each capacitor, taking ΔVab = 16.0 V.
20.0 µF capacitor
µC
6.00 µF capacitor
µC
3.00 µF capacitor
µC
capacitor C
µC
Two conductors having net charges of +14.0 µC and -14.0 µC have a potential difference of 14.0 V between them. (a) Determine the capacitance of the system. F (b) What is the potential difference between the two conductors if the charges on each are increased to +196.0 µC and -196.0 µC? V
Chapter 3 Solutions
College Physics: A Strategic Approach (4th Edition)
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