Two different wire loops are concentric and lie in the same plane. The current in the outer loop is clockwise and increasing with time. The induced current in the inner loop then is

Options

A. clockwise
B. zero
C. counter-clockwise
D. in a direction that depends on the ratio of the loop radii

Explanation

To solve the problem step by step, we will analyze the situation involving two concentric loops, the direction of the current in the outer loop, and the resulting induced current in the inner loop.

### Step 1: Understand the Setup
We have two concentric wire loops that lie in the same plane. The outer loop has a clockwise current that is increasing with time.

**Hint:** Remember that the direction of the current in the outer loop will affect the magnetic field it produces.

### Step 2: Determine the Magnetic Field Direction
The current in the outer loop is clockwise. According to the right-hand rule, the magnetic field produced by a clockwise current will point downwards (into the plane of the loops) at the center of the loops.

**Hint:** Use the right-hand rule to visualize the direction of the magnetic field created by the current in the outer loop.

### Step 3: Analyze the Change in Magnetic Flux
Since the current in the outer loop is increasing, the magnetic field (and thus the magnetic flux) through the inner loop is also increasing. The magnetic flux through the inner loop is given by the product of the magnetic field and the area of the inner loop.

**Hint:** Remember that an increasing magnetic field through a loop indicates that the magnetic flux through that loop is also increasing.

### Step 4: Apply Lenz's Law
Lenz's Law states that the induced current in a loop will flow in such a direction as to oppose the change in magnetic flux through the loop. Since the magnetic flux through the inner loop is increasing in the downward direction (into the plane), the induced current must flow in a direction that creates an opposing magnetic field.

**Hint:** Think about how to oppose an increasing magnetic field that is directed downwards.

### Step 5: Determine the Direction of Induced Current
To oppose the increase in downward magnetic flux, the induced current in the inner loop must flow in the counterclockwise direction. This counterclockwise current will create a magnetic field that points upwards (out of the plane of the loops), opposing the increase in downward magnetic flux.

**Hint:** Visualize the induced current and its effect on the magnetic field to confirm the direction.

### Final Answer
The induced current in the inner loop is **counterclockwise**.