If particle of charge `10^(-12)` coulomb moving along the `hatx` - direction with a velocity `10^(5)m//s` experiences a force of `10^(-10)` newton in `haty` - direction due to magnetic field, then the minimum magnetic field is

Options

A. `6.25 xx10^3` Tesla in `hat z` - direction
B. `10^(-15)` Tesla in `hat z ` - direction
C. `6.25 xx10^(-3)` Tesla in `hat z` - direction
D. `10^(-3)` Tesla in `hat z ` - direction

Explanation

To solve the problem step by step, we will use the formula for the magnetic force acting on a charged particle moving in a magnetic field. The force \( F \) on a charged particle is given by the equation:

\[ F = q \cdot v \cdot B \cdot \sin(\theta) \]

Where:
- \( F \) is the magnetic force (in newtons),
- \( q \) is the charge of the particle (in coulombs),
- \( v \) is the velocity of the particle (in meters per second),
- \( B \) is the magnetic field strength (in tesla),
- \( \theta \) is the angle between the velocity vector and the magnetic field vector.

### Step 1: Identify the known values
From the problem, we have:
- Charge \( q = 10^{-12} \) C
- Velocity \( v = 10^{5} \) m/s
- Force \( F = 10^{-10} \) N
- The particle is moving in the \( \hat{x} \) direction, and the force is in the \( \hat{y} \) direction.

### Step 2: Determine the angle \( \theta \)
Since the particle is moving in the \( \hat{x} \) direction and the force is in the \( \hat{y} \) direction, the angle \( \theta \) between the velocity and the magnetic field must be \( 90^\circ \). Therefore, \( \sin(\theta) = \sin(90^\circ) = 1 \).

### Step 3: Substitute the known values into the formula
Now we can simplify the force equation:

\[ F = q \cdot v \cdot B \cdot \sin(90^\circ) \]

This simplifies to:

\[ F = q \cdot v \cdot B \]

### Step 4: Solve for the magnetic field \( B \)
Rearranging the equation to solve for \( B \):

\[ B = \frac{F}{q \cdot v} \]

### Step 5: Substitute the values into the equation
Substituting the known values:

\[ B = \frac{10^{-10}}{(10^{-12}) \cdot (10^{5})} \]

### Step 6: Calculate the magnetic field
Calculating the denominator:

\[ (10^{-12}) \cdot (10^{5}) = 10^{-7} \]

Now substituting this back into the equation for \( B \):

\[ B = \frac{10^{-10}}{10^{-7}} = 10^{-10 + 7} = 10^{-3} \text{ T} \]

### Final Answer
Thus, the minimum magnetic field \( B \) is:

\[ B = 10^{-3} \text{ T} \text{ or } 1 \text{ mT} \]