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en/9.3.17.md
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| ### Statement | |||
| − | |||
| + | $9.3.17.$ a. The current $I$ goes along a long straight wire perpendicular to the conducting plane and spreads | ||
| + | along it. Determine the magnetic field distribution. | ||
| + | |||
| + | b. A long wire with current $I$ intersects the conducting plane in a direction perpendicular to it. The | ||
| + | current flowing to the plane is $I'$ . Determine the distribution of the magnetic field in this system. | ||
| + | |||
| + | c. The coaxial cable enters the spherical plane as shown in the figure. Find the magnetic field induction | ||
| + | in the entire space. | ||
| + | |||
| ### Solution | |||
| а) | |||
| Let's surround the wire with rings of radius $2\pi x$, above the plane they carry current I and induction $$B = \frac{\mu_0 I}{2\pi x}$$, below the plane there is no current, therefore the induction is zero. | |||
| б) Similarly, over the plane the induction $$B = \frac{\mu_0 I}{2\pi x}$$ under: $$B = \frac{\mu_0 (I-I')}{2\pi x}$$ | |||
| в) Using the same type of circuit, we'll analyze it. Inside the circuit, the current only enters. The answer is $$B = \frac{\mu_0 I}{2\pi x}$$ | |||
| Let's take a wider circuit. The current enters it and the same amount exits $\Longrightarrow$ outside $$B = 0$$ | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||
| unchanged lines 11 | |||
| @@ -1,6 +1,14 @@ | |||
| ### Statement | ### Statement | ||
| $9.3.17.$ a. The current $I$ goes along a long straight wire perpendicular to the conducting plane and spreads | |||
| along it. Determine the magnetic field distribution. | |||
| b. A long wire with current $I$ intersects the conducting plane in a direction perpendicular to it. The | |||
| current flowing to the plane is $I'$ . Determine the distribution of the magnetic field in this system. | |||
| c. The coaxial cable enters the spherical plane as shown in the figure. Find the magnetic field induction | |||
| in the entire space. | |||
| ### Solution | ### Solution | ||
| а) | а) | ||
| Let's surround the wire with rings of radius $2\pi x$, above the plane they carry current I and induction $$B = \frac{\mu_0 I}{2\pi x}$$, below the plane there is no current, therefore the induction is zero. | Let's surround the wire with rings of radius $2\pi x$, above the plane they carry current I and induction $$B = \frac{\mu_0 I}{2\pi x}$$, below the plane there is no current, therefore the induction is zero. | ||
| б) Similarly, over the plane the induction $$B = \frac{\mu_0 I}{2\pi x}$$ under: $$B = \frac{\mu_0 (I-I')}{2\pi x}$$ | б) Similarly, over the plane the induction $$B = \frac{\mu_0 I}{2\pi x}$$ under: $$B = \frac{\mu_0 (I-I')}{2\pi x}$$ | ||
| в) Using the same type of circuit, we'll analyze it. Inside the circuit, the current only enters. The answer is $$B = \frac{\mu_0 I}{2\pi x}$$ | в) Using the same type of circuit, we'll analyze it. Inside the circuit, the current only enters. The answer is $$B = \frac{\mu_0 I}{2\pi x}$$ | ||
| Let's take a wider circuit. The current enters it and the same amount exits $\Longrightarrow$ outside $$B = 0$$ | Let's take a wider circuit. The current enters it and the same amount exits $\Longrightarrow$ outside $$B = 0$$ | ||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | [Insert a concise answer or boxed result] | ||
| unchanged lines 11 | |||