A long, straight wire of radius r carries a current i and is placed horizontally in a uniform magnetic field B pointing vertically upward. The current is uniformly distributed over its cross section. (a) At what points will the resultantant magnetic field have maximum magnitude? What will be the maximum magnitude? (b) What will be the minimum magnitude of the resultant magnetic field?

Explanation

To solve the problem step by step, we will analyze the magnetic field produced by the current in the wire and how it interacts with the external magnetic field.

### Step 1: Understand the Setup
We have a long straight wire of radius \( r \) carrying a current \( I \). The wire is placed horizontally in a uniform magnetic field \( B \) that points vertically upward. The current is uniformly distributed across the wire's cross-section.

### Step 2: Magnetic Field Due to the Wire
The magnetic field \( B_w \) at a distance \( x \) from the center of a long straight wire carrying current \( I \) is given by the formula:
\[
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