Physics
Physics
1st Edition
Walker
ISBN: 9780133256925
Textbook solutions

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Page 712: Practice Problems

Exercise 6
Step 1
1 of 1
The magnitude of the total electric field will be the same ,this is because the vertical component will remain as it is ,and the horizontal component will have same magnitude but opposite direction which will charge the direction of the net field but not the total magnitude
Exercise 7
Step 1
1 of 2
$text{color{#4257b2}Picture the Problem and Strategy}$

The situation, as we see in our sketch, is basically the same as Example 20.4, with the only difference that the $x$ component of the electric field now is two times larger and points in the opposite direction. This is an expected result, as we changed the sign of the charge on the $x$ axis and doubled its magnitude (remember that the magnitude of the electric field is directly proportional to the magnitude of the charge producing it). So, the calculations are basically the same except that we now replace $E_x$ by $2E_x$, which, of course, changes the magnitude of the total electric field.

$text{color{#4257b2}Solution}$

The $y$ component of the electric field remains unchanged: $E_y = 8.0times10^4$ N/C. Because $E = kq/r^2$ and $q$, on the $x$ axis, doubles in magnitude, we obtain

$$
E_x = 2times(8.0times10^4;mathrm{N/C}) = 1.6times10^5;mathrm{N/C}
$$

Hence, the total electric field is

$$
begin{align*}
E_{rm total} &= sqrt{E_x^2 + E_y^2}\
&= sqrt{(8.0times10^4;mathrm{N/C})^2 + (1.6times10^5;mathrm{N/C})^2}\
&= 1.8times10^5;mathrm{N/C}
end{align*}
$$

Exercise scan

Result
2 of 2
$$
1.8times10^5;mathrm{N/C}
$$
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