Question

Two particles A and B have equal charges but different masses M_A and M₈. After being accelerated through same potential difference enter the region of uniform magnetic field and describe the path of radii R_A and R_B respectively. Then M_A : M_B is ______.

Options

• `"R"_"B"/"R"_"A"`

• `("R"_"A"/"R"_"B")^2`

• `"R"_"A"/"R"_"B"`

• `("R"_"B"/"R"_"A")^2`

Answer 1

Two particles A and B have equal charges but different masses M_A and M₈. After being accelerated through same potential difference enter the region of uniform magnetic field and describe the path of radii R_A and R_B respectively. Then M_A : M_B is `underline(("R"_"A"/"R"_"B")^2)`.

Explanation:

Since the two particles have same charge and are accelerated through the same potential difference, they have same kinetic energy k(=qV). Ifp is the momentum then

k = `"P"^2/"2m" or "P" = sqrt"2mk"`.

The radius of the circular path in a magnetic field is given by

R = `"p"/"qB" = sqrt"2mk"/"qB"`

`therefore "R" prop sqrt"m"`

or `"M"_"A"/"M"_"B" = "R"_"A"^2/"R"_"B"^2`