Charges of −4q are fixed to diagonally opposite corners of a square. A charge of + 5q is fixed to one of the remaining corners, and a charge of + 3q is fixed to the last corner. Assuming that ten electric field lines emerge from the + 5q charge, sketch the field lines in the vicinity of the four charges.

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To sketch the electric field lines in the vicinity of the four charges, we need to understand the behavior of electric field lines.

The electric field lines emerge from positive charges and terminate on negative charges. The density of the field lines indicates the strength of the electric field. The field lines never intersect each other.

Now let's consider the given scenario:

There are four charges:
1. Two negative charges of -4q fixed at diagonally opposite corners of the square.
2. One positive charge of +5q fixed at one of the remaining corners.
3. One positive charge of +3q fixed at the last corner.

We are told that ten electric field lines emerge from the +5q charge. This means that the strength of the electric field produced by the +5q charge is stronger compared to the other charges.

Here are the steps to sketch the electric field lines:

1. Start by drawing a square to represent the charges. Label the charges and their magnitudes at the respective corners.
- Negative charge of -4q at one corner.
- Negative charge of -4q at the diagonally opposite corner.
- Positive charge of +5q at one corner (different from negative charges).
- Positive charge of +3q at the remaining corner (different from other charges).

2. Since ten field lines emerge from the +5q charge, draw ten lines spreading out radially from the +5q charge in all directions. Remember that the density of field lines represents the strength of the electric field, so you can make the lines closer or farther apart to indicate a stronger or weaker field respectively.

3. Now consider the negative charges. Electric field lines originate from them but terminate on other charges. Draw a few lines originating from the negative charges. These lines will be attracted to the positive charges nearby, resulting in bending or curving.

4. Observe that the electric field lines originating from the negative charges will terminate on the positive charges nearby, i.e., they will approach and end on the +5q and +3q charges.

5. Continue this process until you have a sketch that represents the electric field lines around the charges in the given scenario.

Remember to follow the general principles:
- Electric field lines always emerge from positive charges.
- Electric field lines terminate on negative charges.
- Electric field lines never intersect one another.

By following these steps, you can sketch the field lines in the vicinity of the four charges and visualize the electric field around them.