Question

Two charges 4q and q are placed 30 cm apart. At what point value of electric field will be 0

Answer 1

Heya!!

let the Electric Field is zero at point p at a distance of x from charge 4q.

Electric Field at point p due to charge 4q is

E = (k × 4q)/x²

Electric Field at point p due to charge q is

E' = (k × q)/( 30 - x)²

E = E' ( For zero Electric field at point p)

( k × 4q )/x² = ( k × q )/( 30 - x )²

4(30 - x )² = x²

4 ( 900 + x² - 60x ) = x²

3600 + 4x² - 240x = x²

3x² - 240x + 3600 = 0

x² - 80x + 1200 = 0

x² - 60x - 20x + 1200 = 0

x ( x - 60 ) - 20 ( x - 60 ) = 0

x = 20 OR x = 60

x = 60 will be rejected becoz distance between two charges is 30cm

So, x = 20cm

So, the Electric Field is zero at a distance of 20cm from charge 4q. or at a distance of 10cm from charge q.