Derive an expression for electric potential due point charge at distance r. Also plot graph of potential V with distance r.
Answers
Answer:
How do you solve fractions step by step?
Conversion a mixed number 16 3/
8
to a improper fraction: 16 3/8 = 16 3/
8
= 16 · 8 + 3/
8
= 128 + 3/
8
= 131/
8
To find new numerator:
a) Multiply the whole number 16 by the denominator 8. Whole number 16 equally 16 * 8/
8
= 128/
8
b) Add the answer from previous step 128 to the numerator 3. New numerator is 128 + 3 = 131
c) Write a previous answer (new numerator 131) over the denominator 8.
Sixteen and three eighths is one hundred thirty-one eighths
Conversion a mixed number 9 5/
8
to a improper fraction: 9 5/8 = 9 5/
8
= 9 · 8 + 5/
8
= 72 + 5/
8
= 77/
8
To find new numerator:
a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/
8
= 72/
8
b) Add the answer from previous step 72 to the numerator 5. New numerator is 72 + 5 = 77
c) Write a previous answer (new numerator 77) over the denominator 8.
Nine and five eighths is seventy-seven eighths
Subtract: 131/
8
- 77/
8
= 131 - 77/
8
= 54/
8
= 2 · 27/
2 · 4
= 27/
4
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the next intermediate step, , cancel by a common factor of 2 gives 27/
4How do you solve fractions step by step?
Conversion a mixed number 16 3/
8
to a improper fraction: 16 3/8 = 16 3/
8
= 16 · 8 + 3/
8
= 128 + 3/
8
= 131/
8
To find new numerator:
a) Multiply the whole number 16 by the denominator 8. Whole number 16 equally 16 * 8/
8
= 128/
8
b) Add the answer from previous step 128 to the numerator 3. New numerator is 128 + 3 = 131
c) Write a previous answer (new numerator 131) over the denominator 8.
Sixteen and three eighths is one hundred thirty-one eighths
Conversion a mixed number 9 5/
8
to a improper fraction: 9 5/8 = 9 5/
8
= 9 · 8 + 5/
8
= 72 + 5/
8
= 77/
8
To find new numerator:
a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/
8
= 72/
8
b) Add the answer from previous step 72 to the numerator 5. New numerator is 72 + 5 = 77
c) Write a previous answer (new numerator 77) over the denominator 8.
Nine and five eighths is seventy-seven eighths
Subtract: 131/
8
- 77/
8
= 131 - 77/
8
= 54/
8
= 2 · 27/
2 · 4
= 27/
4
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the next intermediate step, , cancel by a common factor of 2 gives 27/
4
. How do you solve fractions step by step?
Conversion a mixed number 16 3/
8
to a improper fraction: 16 3/8 = 16 3/
8
= 16 · 8 + 3/
8
= 128 + 3/
8
= 131/
8
To find new numerator:
a) Multiply the whole number 16 by the denominator 8. Whole number 16 equally 16 * 8/
8
= 128/
8
b) Add the answer from previous step 128 to the numerator 3. New numerator is 128 + 3 = 131
c) Write a previous answer (new numerator 131) over the denominator 8.
Sixteen and three eighths is one hundred thirty-one eighths
Conversion a mixed number 9 5/
8
to a improper fraction: 9 5/8 = 9 5/
8
= 9 · 8 + 5/
8
= 72 + 5/
8
= 77/
8
To find new numerator:
a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/
8
= 72/
8
b) Add the answer from previous step 72 to the numerator 5. New numerator is 72 + 5 = 77
c) Write a previous answer (new numerator 77) over the denominator 8.
Nine and five eighths is seventy-seven eighths
Subtract: 131/
8
- 77/
8
= 131 - 77/
8
= 54/
8
= 2 · 27/
2 · 4
= 27/
4
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the next intermediate step, , cancel by a common factor of 2 gives 27/
4
.
In words - one hundred thirty-one eighths minus seventy-seven eighths = twenty-seven quarters.
In words - one hundred thirty-one eighths minus seventy-seven eighths = twenty-seven quarters.
.
In words - one hundred thirty-one eighths minus seventy-seven eighths = twenty-seven quarters.
Answer:
charge q, As we move from point A, at distance rA from the charge q, to point B, at distance rB from the charge q, the change in electric potential is
ΔV
BA
=V
B
−V
A
=−∫
A
B
E.ds
E.ds=[k
r
2
q
]
r
^
.ds
r
^
.ds=dr
Only the radial distance r determines the work done or the potential. We can move through any angle we like and, as long as the radial distance remains constant, no work is done or there is no change in the electric potential.
ΔV
BA
=V
B
−V
A
=−∫
r
A
r
B
Edr=−∫
r
A
r
B
[k
r
2
q
dr]
ΔV
BA
=V
B
−V
A
=−kq[(−1)r
−1
]
r
A
r
B
ΔV
BA
=V
B
−V
A
=kq[
r
B
1
−
r
B
1
]
This is the change in electric potential due to a point charge as we move from rA to rB.
We could ask about the change in electric potential energy as we move a charge q' from radius rA to rB due to a point charge q
ΔU
BA
=kq
′
q[
r
B
1
−
r
A
1
]
As with gravitational potential energy, it is more convenient -- and, therefore, useful -- to talk about the electric potential energy or the electric potential relative to some reference point. We will choose that reference point to be infinity. That is,
r
A
=∞
That means we can then write the electric potential at some radius r as V=kq
r
1