Chapter 23, Problem 105A

(a)

To determine

The effect on magnitude of field strength in the given situation.

Explanation of Solution

Given:

Electric field strength, E due to charge Q at distance d .

Distance d is tripled.

Formula Used:

Electric field:

$E=\frac{kQ}{d^2}$

Here, k is the Coulomb’s constant, Q is the charge and dis the distance.

Calculation:

$E\propto \frac{1}{d^2}$

When, d is tripled, electric field strength reduces by 9 times.

Conclusion:

The field strength decreases by 9 times when d is increased by 3 times.

(b)

To determine

The effect on magnitude of field strength in the given situation.

Explanation of Solution

Given:

Electric field strength, E due to charge Q at distance d .

Charge Q is tripled.

Formula Used:

Electric field:

$E=\frac{kQ}{d^2}$

Here, k is the Coulomb’s constant, Q is the charge and dis the distance.

Calculation:

$E\propto Q$

When, Q is tripled, electric field strength is also tripled at distance d .

Conclusion:

The field strength increases by 3 times when Q is increased by 3 times.

(c)

To determine

The effect on magnitude of field strength in the given situation.

Explanation of Solution

Given:

Electric field strength, E due to charge Q at distance d .

Charge Q is tripled.

Formula Used:

Electric field:

$E=\frac{kQ}{d^2}$

Here, k is the Coulomb’s constant, Q is the charge and dis the distance.

Calculation:

$E\propto Q$

$E\propto \frac{1}{d^2}$

When, Qand d are tripled, electric field strength is tripled due to tripled charge and reduced by 9 times due to tripled distance. So, overall, the field strength decreases by 3 times.

Conclusion:

The field strength decreased by 3 times.

(e)

To determine

The effect on magnitude of field strength in the given situation.

Explanation of Solution

Given:

Electric field strength, E due to charge Q at distance d .

Charge Q , distance d and test charge $q\text{'}$ are tripled.

Formula Used:

Electric field:

$E=\frac{kQ}{d^2}$

Here, k is the Coulomb’s constant, Q is the charge and dis the distance.

Calculation:

The field strength does not depend on test charge. Thus, tripling the test charge would not affect the it.

When, Q and d are tripled, electric field strength is tripled due to tripled charge and reduced by 9 times due to tripled distance. So, overall, the field strength decreases by 3 times.

Conclusion:

The field strength decreased by 3 times.